Cwm Taf Health Board and Macmillan Cancer Support are seeking planning permission at the Llantrisant site.
The charity will pay £5m towards the unit.
With eight beds, it would provide inpatient, outpatient and day palliative care for incurable cancer and other conditions.
Macmillan's proposed contribution, which is subject to planning approval, would be its biggest single investment in Wales.
Dr Ian Back, consultant in palliative medicine at Cwm Taf University Health Board, said: "A new state-of-the-art specialist unit would provide patients with the high-quality care they need in a comfortable environment for both them and their loved ones.
"Building the new unit at Royal Glamorgan Hospital will also ensure that patients have access to specialist tests and treatment more easily without the need for unnecessary transfers between hospitals when they are often too unwell."
Palliative care for cancer patients in the county is currently provided at Pontypridd Cottage Hospital.
This means patients need to be transferred to Royal Glamorgan Hospital to access specialist tests and treatments, which the health board said can be "difficult and distressing".
Susan Morris, head of services for Macmillan Cancer Support in Wales, said: "After extensive consultation with staff and patients, the unit would be designed using Macmillan's expertise and understanding of the needs of people with cancer and their families, including a kitchen and communal areas where they can spend time together."
If the plans are approved, work is expected to start later this year with the centre potentially opening in late 2018 or early 2019.
Plans for a £6.75m specialist cancer care unit at Royal Glamorgan Hospital in Rhondda Cynon Taff have been unveiled.