Bury's two MPs are part of a working group calling for the expelled club to be reinstated in the EFL as a Sky Bet League Two side for the 2020/21 season.
The former League One club and two-time FA Cup winners were kicked out of the EFL last week.
Meanwhile, an international consortium has £7m in the bank and is ready to complete a takeover of Bury, if the EFL agrees to reinstate the club, Sky Sports News understands.
James Frith MP (Bury North) and Ivan Lewis MP (Bury South) have released a joint statement, along with Manchester mayor Andy Burnham and supporters society Forever Bury, who are all campaigning to try and secure the club's status in the EFL for next season.
It read: "We are establishing a working group to develop a proposal to the Football League that would allow Bury to be admitted to Sky Bet League Two for the start of the 2020/21 season, subject to the submission of a credible plan to rebuild Bury FC before the end of this year.
"First, we will work to develop a clear proposal to the English Football League, by September 20, that will allow us the opportunity to work towards re-entry to League Two.
"Second, if the EFL agree to that proposal, we will then work on a credible plan to rebuild the club, which all signatories to this statement will feel able to endorse.
"Third, if that credible plan fails to emerge within the deadline then we accept the EFL's right to impose their original decision.
"We are pleased that Steve Dale has agreed to give us a short period of time to identify a suitable new owner for the club - we ask in good faith that the current owner allows us the opportunity to take forward this proposal."