The loggerhead turtle, known as Terri, was found on a beach in Jersey 12 days ago, and has since been treated by the New Era Veterinary Hospital.
Terri is currently housed in a special water tank at a fish suppliers, but vets say she needs a warmer climate.
Vet Peter Haworth, who launched the campaign, said: "She wants to go free".
So far more than £2,500 has been raised by the funding campaign website, but Mr Haworth said they need to hit the total within the next week.
He said: "We're not stupid...it's a huge huge amount of money but we were given a very ill animal to try and save."
The campaign group Get Terri the Turtle Back Home said there were no direct flights to the Canary Islands until late February, by which point the turtle might have died.
The group said chartering a private jet at a cost of £22,000 was "the most reliable way to ensure her a future", and no-one was profiting from the campaign.
The turtle's medication expenses have been covered by the New Era Veterinary hospital, while her water temperature has been regulated by The Fresh Fish Company.
Mr Haworth said Terri was now "very strong" but "the water depth we can have her in here isn't deep enough to encourage her to eat".
Mr Haworth said if the target was not reached they would try to send the turtle to an aquarium in the UK.
An endangered turtle will fly by private jet to the Canary Islands at a cost of £22,000, if an online fundraising campaign succeeds.