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.

After a nervous start, the Gulls grew into the game and started to apply pressure, which nearly paid off in the 14th minute when a powerful shot from Brett Williams struck a post.
Luke Young forced a good save from Owen Evans and later went close with a couple of first-half free-kicks.
The Gulls started the second half purposefully and finally breached the visitors' defence in the 58th minute when skipper Aman Verma headed home a free-kick after Jordan Lee had been brought down by Mark Gray.
Giancarlo Gallifuoco had a goal disallowed in the 65th minute, but the Gulls ensured they will be back in the National League next season when Myles Anderson headed home two minutes from time.
Match report supplied by the Press Association.
Match ends, Torquay United 2, North Ferriby United 0.
Second Half ends, Torquay United 2, North Ferriby United 0.
Substitution, North Ferriby United. Jordan Douglas replaces Owen Evans.
Substitution, Torquay United. Shaun Harrad replaces Brett Williams.
Goal!  Torquay United 2, North Ferriby United 0. Myles Anderson (Torquay United).
Substitution, Torquay United. Sam Chaney replaces Jordan Lee.
Substitution, North Ferriby United. George Bell replaces Reece Thompson.
Substitution, North Ferriby United. Jordan Cooke replaces Taron Hare.
Substitution, Torquay United. Dan Sparkes replaces Jamie Reid.
Goal!  Torquay United 1, North Ferriby United 0. Aman Verma (Torquay United).
Second Half begins Torquay United 0, North Ferriby United 0.
First Half ends, Torquay United 0, North Ferriby United 0.
First Half begins.
Lineups are announced and players are warming up.

City council leader Lib Dem Simon Cook will tell a conference an arena on the site of the old diesel depot site is a crucial part of the zone.
He stressed although it was early days potential operators believe its size would attract many good quality shows.
Mr Cook said there was a risk a larger version would be built in Cardiff if the Bristol arena did not go ahead.
"We've fallen behind Cardiff too often in the past. It is really time to grab the opportunity and go for it.
"There is a very big interest in an arena for Bristol... we're absolutely determined to deliver it," he added.
It is believed the arena would cost up to Â£80m to build, some of which will come from the government's City Deal fund.
Several plans for an entertainment arena have been put forward since 2003 but the idea was dropped in 2007 when costs rose to Â£86m.
Then in 2009, plans for a 15,000-seater music and sport venue were proposed with a second site at Ashton Vale close to where Bristol City Football Club wants to build a new stadium.
The city's biggest music venue is the famous Colston Hall, which can hold about 2,000 people.
Plans for a £6.75m specialist cancer care unit at Royal Glamorgan Hospital in Rhondda Cynon Taff have been unveiled.
[NEXT_CONCEPT]
Torquay guaranteed another season in the National League with a well-deserved victory against relegated North Ferriby at Plainmoor.
[NEXT_CONCEPT]
A 12,000-seater music venue on the Temple Meads Enterprise Zone in Bristol is possible by 2016, the council says.