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."
At present, application for re-entry into the English league system must be submitted to the Football Association, which would then determine which division the club will play in.
https://www.bbc.co.uk/sport/football/49569697