Sports Minister Tracey Crouch is to consider drafting in a mediator to help resolve the crisis engulfing Coventry.
The Tory frontbencher faced calls from Labour's Jim Cunningham, MP for Coventry South, to appoint an "eminent figure", such as a judge, to "get all sides together" and resolve the problems facing the Sky Blues.
MPs heard the deal allowing City to play at the Ricoh Arena expires at the end of the 2017/18 season, with talks to reach an agreement having broken down.
Cunningham added a long-term solution "remains far away", telling MPs: "The threat of the club once again moving out of the city remains."
The club previously spent time playing homes games in Northampton following a long-running dispute between its owner Sisu and then ground owner Arena Coventry Limited.
Rugby union side Wasps have since taken over the stadium after relocating.
Coventry sit bottom of the League One table, with just one win in their opening 11 games.
On the proposal for a mediator to resolve the issues facing the club, Crouch told Cunningham during a Westminster Hall debate: "One of the most frustrating things I think sometimes about the sports minister brief, and also in terms of football, is actually there's a lot of things that happen within football that should have nothing to do with Government.
"I regularly get contacted by supporters of various football clubs, of which Coventry City is one, where they wish for the Government to intervene, where they wish for the minister to get personally involved and that is incredibly difficult to do because ultimately it's not a matter for the Government to intervene on these things.
"However, I completely hear what you say in terms of trying to ensure that there is somebody that would mediate between the parties.
"And if it has got to that point where the relationship is so broken that the parties can't come together and come to agreement then that is something we'll take away and I will consider in great detail."
Crouch suggested Tory MP Damian Collins, who has campaigned for greater supporter involvement in football clubs and for an overhaul of how the game is regulated, may wish to consider if he could play a role.
She said "someone outside the political arena" may instead be appropriate, adding: "Ultimately, this is an issue for the football authorities and they need to come together to try and sort this out."
Cunningham, intervening, told Crouch: "I understand ministers can't get involved, they don't want to get involved, but ministers do have the authority to appoint somebody of some standing to bring both sides together.
"I think the fans would welcome that and the fans have been very constructive... I accept ministers very often get lots of demands from football fans and all that goes with that.
"But this is far too serious now. This has been going on for five or six years and something has got to be done about it."