Party leaders at Bristol City Council have written to both sides involved in a dispute over the site of a proposed new stadium to seek a compromise.
Bristol City FC wants to build a new 30,000-seater stadium at Ashton Vale.
But following an application by residents, an independent planner recommended the area be registered as a town green, preventing new development.
The Liberal Democrat-run council has already approved the planning application for the stadium.
Council leader Barbara Janke, Labour leader Helen Holland and Conservative leader Geoff Gollop said they had asked the applicants for town green status and the landowners to consider whether both the football stadium and using part of the site for recreation was possible.
A statement issued by the applicants said: "The applicants are happy to talk to the landowners to discuss potential ways of resolving this matter.
"Representatives of the applicants have undertaken such talks in the past with little success but we are happy to try again."
The letter from the leaders says: "It is clear from this process that the application has polarised public and media opinion making any potential eventual decision unacceptable to one or other party and also sectors of the community.
"As leaders of the city council we find this situation to be one of great concern, both from the perspective of the impact the situation is having on cohesion in the local community and with regard to the difficulties the situation poses for the future growth and economy of Bristol as the regional centre of the West of England."
They said they have given the parties seven days to respond.
The final decision on town green status rests with Bristol City Council.
Mr Gollop said: "If the arguments continue, the council will face a legal challenge from the losing side, which will cost the council and therefore the council tax payer significant sums of money that it cannot afford.
"Mediation has to be the sensible way forward."