They are due to visit Hillsborough on Tuesday August 13, with the EFL believed to want to offer a week’s notice to any club affected by the Shakers’ ongoing financial struggles.
Bury, promoted as runners-up from League Two last season, must prove to the EFL that they have the means to fund themselves going forward before they are allowed to fulfil fixtures.
With no precedent set for this eventuality in League Cup matches, it is unclear whether Wednesday would be awarded a bye in the event of a suspension.
The League One side’s opening day match against MK Dons this weekend has been suspended by the EFL, with a decision on the club’s following fixture against Accrington Stanley – due to be played on August 10 – to be made this Saturday.
The authority are understood to be working closely with both Bury and cash-strapped Bolton, who have been given permission to fulfil their opening day match against Wycombe this weekend.