The company is working on technology that combines disease-detecting nanoparticles, which would enter a patient's bloodstream via a swallowed pill, with a wrist-worn sensor.
The idea is to identify slight changes in the person's biochemistry that could act as an early warning system.
The work is still at an early stage.
Early diagnosis is the key to treating disease. Many cancers, such as pancreatic, are detected only after they have become untreatable and fatal.
There are marked differences between cancerous and healthy tissues.
Google's ambition is to constantly monitor the blood for the unique traces of cancer, allowing diagnosis long before any physical symptoms appear.
The project is being conducted by the search company's research unit, Google X, which is dedicated to investigating potentially revolutionary innovations.
It marks the firm's latest shift into the medical sector following its work on glucose-measuring contact lenses for patients with diabetes and the acquisition of a start-up that developed a spoon to counteract the tremors caused by Parkinson's disease.
Google has also bought stakes in Calico, an anti-ageing research company, and 23andMe, which offers personal genetic-testing kits.
The diagnostic project is being led by Dr Andrew Conrad, a molecular biologist who previously developed a cheap HIV test that has become widely used.
"What we are trying to do is change medicine from reactive and transactional to proactive and preventative," he told the BBC.
"Nanoparticles... give you the ability to explore the body at a molecular and cellular level."
Google is designing a suite of nanoparticles which are intended to match markers for different conditions.
They could be tailored to stick to a cancerous cell or a fragment of cancerous DNA.
Or they could find evidence of fatty plaques about to break free from the lining of blood vessels. These can cause a heart attack or stroke if they stop the flow of blood.
Another set would constantly monitor chemicals in the blood.
High levels of potassium are linked to kidney disease. Google believes it will be possible to construct porous nanoparticles that alter colour as potassium passes through.
"Then [you can] recall those nanoparticles to a single location - because they are magnetic - and that location is the superficial vasculature of the wrist, [where] you can ask them what they saw," said Dr Conrad.
Unattached nanoparticles would move differently in a magnetic field from those clumped around a cancer cell.
In theory, software could then provide a diagnosis by studying their movements.
As part of the project, the researchers have also explored ways of using magnetism to concentrate the nanoparticles temporarily in a single area.
The tech company's ambition is ultimately to create a wristband that would take readings of the nanoparticles via light and radio waves one or more times a day.
Prof Paul Workman, chief executive of the Institute of Cancer Research in London, told the BBC News website: "In principle this is great. Any newcomers with new ideas are welcome in the field.
"There is an urgent need for this. If we can detect cancer or other diseases earlier, then we can intervene with either lifestyle changes or treatment.
"How much of this proposal is dream versus reality is impossible to tell because it is a fascinating concept that now needs to be converted to practice."
His team at the institute is investigating cancer cells and cancer DNA in the blood as new methods of diagnosis and planning treatment.
He did warn Google that a diagnosis could increase anxiety and lead to unnecessary treatment, so there needed to be "very careful and rigorous analysis" before this type of blood monitoring could be used widely.
The scheme is being made public because Google is now seeking to  establish partnerships.
But Dr Conrad sought to play down the idea that his firm wanted to run a search tool for the human body, alongside the one it already offers for the internet.
"We are the inventors of the technology but we have no intentions of commercialising it or monetising it in that way," he said.
"We will license it out and the partners will take it forward to doctors and patients.
"These are not consumer devices. They are prescriptive medical devices, and you know that doctor-patient relationships are pretty privileged and would not involve Google in any way."
Analysis: James Gallagher, health editor
From searching the internet to searching your blood, Google certainly has high ambitions. But is it feasible?
The basic principles are sound and mirror the work already taking place around the world.
Many research groups are looking at bits of cancer floating in the blood as a better way of diagnosing the disease and also to assess which tumours are more aggressive.
But Google will have to address concerns around "false positives", when healthy people are told they are ill.
These have plagued the PSA test for prostate cancer, as PSA levels can soar even when cancer is absent.
There is also the issue of "over-diagnosis". Who needs treating even if a condition is discovered?
There is continuing controversy around breast cancer screening: for every life saved, three women have invasive treatment for a cancer that would never have proved fatal.
Screening the body for disease is littered with dangers, and if it is not done carefully, it could make hypochondriacs out of all of us.
The nanoparticle project is the latest so-called "moonshot" to originate from Google X.
Other schemes include the firm's driverless car effort and Project Loon, an attempt to provide internet access to remote areas via a network of high-altitude weather balloons.
While such ideas have the potential to make money, there is also a high risk of failure, and Google X acknowledges that several of its ideas have been ditched before being made public.
One analyst commented that its parent was in a rare position to make such investments.
"Under normal circumstances this is the kind of thing that would worry investors because such projects are too long-term and the miss rate is too high," said Cyrus Mewawalla, from CM Research.
"But because Google's core search business is currently so strong, shareholders are not worried at the moment and are allowing the firm to take a gamble."
Analysis: Leo Kelion, technology desk editor
Google's diagnostic project may never come to fruition, but its significance lies in the fact it represents part of a wider push by the firm into health tech.
Bearing in mind this is already a crowded sector, it begs the question: why?
The search firm denies that it wants to run its own diagnosis service, with all the privacy headaches that would entail, but the patents it creates along the way could prove lucrative.
No doubt the fact that co-founder and Google X chief Sergey Brin has been told that a gene mutation has increased his likelihood of contracting Parkinson's has also focused efforts.
And the company clearly believes its expertise in "big data" analysis and its freedom to focus on giant leaps forward, rather than incremental steps, plays to its advantages.
It's worth remembering that another much hyped health idea, Google Flu Trends - which aimed to predict the spread of the virus based on internet searches - has been dubbed a failure by some after researchers said it had overestimated the number of cases in 100 out of 108 weeks.
And US health watchdogs banned Google-backed 23andme from selling the the heath data part of its genetic screening kits last year.
On the other hand, Google's "smart lens" for diabetics shows promise, with Swiss firm Novartis stepping up to license the technology in July.
And the forthcoming Android Fit platform, designed to harness data from other apps and wearables, has a good chance of success given the huge number of people using the operating system.
Google is aiming to diagnose cancers, impending heart attacks or strokes and other diseases, at a much earlier stage than is currently possible.