Bury North MP James Frith has said he plans to put forward a proposal to the EFL by 20 September in a bid to have Bury reinstated to League Two in 2020-21.
The Shakers, who were in League One, were expelled from the EFL last week.
“We believe it is time to put forward a fair resolution that the club, the town and the wider game can unite around,” Frith said.
Mayor of Manchester Andy Burnham has also backed the proposal.
He told BBC sports editor Dan Roan: “We need to try and get a way forward for Bury FC that the fans, town and wider football family can get behind, and that’s what we’ve been discussing.
“We recognise the mismanagement that has put Bury in this situation, so we understand EFL needs to take action, but feel the punishment is unduly harsh and what we’ve developed today is a proposal to try and persuade the other clubs that Bury should remain a Football League club, but entering League Two for next season.”
Bury’s 125-year membership of the Football League was ended after a proposed takeover bid from potential owners C&N Sporting Risk collapsed.
Following takeover talks with club owner Steve Dale that had moved slowly all summer, the Gigg Lane club had already cancelled their first five league games and been thrown out of the EFL Cup, for non-fulfilment of a first-round fixture.
Bury’s expulsion means that three clubs, rather than four, will be relegated from League One this season and just one, instead of two, from League Two.