QPR's Disabled Supports Association (DSA) has called on the club and Hammersmith and Fulham Council to work together to find a new home for the club within the borough.
The Shepherd's Bush club has been searching for a move away from Loftus Road and last year identified the Linford Christie Stadium as a possible site to relocate.
It has argued its current ground, which has been its home for the over a century, is out of date compared to other stadiums.
There is also particularly poor access and facilities for disabled supporters, says the club, with a limited scope for improvement.
DSA committee member Oliver Greene went to his first Rs game in 1966 and uses a wheelchair.
He said: "The club does its best they can do to look after disabled supporters, but with Loftus Road being so old and small it is a big hindrance.
"The disabled toilets need to be improved but there just isn't the space.
"And the small distance between the hoardings and wheelchair users' feet means they get knocked when fans walk past, which can be very painful."
Bernie Ginty is a DSA member who is in his 52nd season supporting the club.
He said: "The entrances and concourses are far too small, especially if you're in a wheelchair.
"And it's too crowded to get food and drink at half time, so the club is missing out on that potential revenue from people like me.
"I could never support any other team but I do pray the club get a new stadium soon - if not for me then kids who are hovering between QPR and other cluibs.
"These kids are our future so we need a stadium to support their support."
Disability charity Level Playing Field recommends that a ground the size of Loftus Road should have 140 wheelchair spaces, but QPR currently has just 34, despite adding an extra 10 before the start of the 2017/18 stadium.
In addition, many hospitality areas at the ground are completely inaccessible to anyone in a wheelchair.
DSA chairman Julie Hampton is ambulant disabled and urged the club to consider accessibility issues as they develop plans for a new stadium.
"I know its almost, if not, impossible for Loftus Road to be adapted for more disabilities and more space.
"If I want to get a hot drink or use the toilet facilities at halftime I miss at least 10 minutes of the game.
"It would be very nice if when a new stadium is built some of these problems are considered."
Fan Karen Hampshire has been a driving force behind the new group. She said: "Like every QPR fan I love going to Loftus Road, but sadly our stadium is now well past its sell-by date.
"Like many other older stadiums, the wheelchair places are all at pitch level, which is not a great vantage point, and the narrow seats and lack of leg room means it can be claustrophobic for fans with learning difficulties.
"I'm delighted that the club is listening to us about what we would like to see at a new stadium based on our experiences elsewhere in the country.
"We hope they can work with the local authority to keep QPR in Hammersmith and Fulham by moving to a sustainable new home as close as possible to Loftus Road."
QPR chief executive Lee Hoos said: "We want QPR to be open to everyone.
"We look forward to working with the DSA to find a new home for the club in the borough that provides much better facilities than we ever could at Loftus Road.”
The option to relocate half-a-mile away to Linford Christie Stadium, home of Thames Harriers athletics club, is being explored by QPR.
It is continuing to hold consultations with residents and fans and is in informal talks with Hammersmith and Fulham Council, but no formal proposal has been put forward.
Hammersmith and Fulham is also home to Chelsea and Fulham Football Clubs.
A spokesman for the council said: "We are immensely proud that three world-class football clubs call Hammersmith and Fulham their home and we will do whatever we can to help the clubs continue to give back to their fans and the community.
"We are currently helping QPR identify sites and will make sure they get the support they need as they work with local residents on a new stadium plan.”
Keep up to date with the latest news in west London via the free getwestlondon app.
You can even set it to receive push notifications for all the breaking news in your area