The English Football League is to discuss Bury's future with its member clubs following efforts to reinstate the Shakers in League Two next season, reports BBC Sport.
Bury were expelled from the EFL on 27 August after a failed takeover bid by C&N Sporting Risk.
Bury North MP James Frith has called for the Shakers to re-enter in the fourth tier for the 2020-21 season.
Meanwhile, Greater Manchester Police has said it is investigating an allegation of fraud involving the club.
No arrests have been made and inquiries are ongoing.
In a statement, the EFL said the "only current established procedure" for entry to League Two is promotion through the National League.
However, it added that "in acknowledgement of the extreme nature of the problems" at Bury, the EFL board had "agreed it is appropriate to discuss the matter with member clubs" and those talks will take place in the coming weeks.
The statement concluded: "Prior to formal consideration by any league competition of an eventual application from Bury FC to return to league football, clear evidence would be required of the club's financial viability and its ability to fulfil its ongoing commitments."