Bury owner Steve Dale says he will consider selling financially embattled League One club after staff 'implored' him to accept a new offer.
Shakers staff issued a statement on Monday saying interest had come in for the club, which could face having a fourth game successive game postponed.
Minutes earlier the EFL gave Bury until 09:00 BST on Tuesday to show how it will pay creditors.
If they cannot, Saturday's game with Gillingham will be suspended.
"Due to the agenda with the EFL, my health and recent events at the club I can confirm I am happy to pass the club on to the next custodian. For an agreed consideration and them being the right fit for Bury," Dale told BBC Radio Manchester in a statement.
Bury are yet to play a game this season after League One matches against MK Dons and Accrington, as well as Tuesday's League Cup match against Sheffield Wednesday, were suspended because of the crisis at Gigg Lane.
Dale had previously said he would not sell the club until financial stability had been restored.
The statement from Bury staff posted on the club website read: "We have received an offer for the sale of Bury Football Club, one that we all at the club believe is a very good offer.
"This offer is the only lifeline for the future of the club and we implore Steve Dale to accept it, as it has the full backing of all of the senior staff at Bury FC."
Shakers' EFL future remains in doubt
Bury have been given until 23 August to avoid being expelled from the English Football League.
The league says it has still to get satisfactory evidence about how Bury will meet their commitments to football creditors, those outlined in their Company Voluntary Arrangement (CVA) or details how the club will be funded this season. Dale denies that claim.
"We remain disappointed that we are still not in a position to reach a successful conclusion with Mr Dale, but will continue to work diligently in an effort to receive the information we require," said EFL executive chair Debbie Jevans.
"The real threat of Bury's EFL membership being withdrawn still exists, a situation nobody - including this board - wants to see and I sincerely hope we can find a way through these challenging circumstances for the benefit of all those who have an association with the club."
Within minutes of the EFL setting a 15-hour deadline for those details, Bury released a three-line statement that said a buyer had come forward with a takeover bid.
Bury's summer of turmoil
Last week, the 134-year-old club said they were "confident" of remaining in the EFL despite the threat of expulsion.
The Shakers, who won promotion from League Two last season, have already been given a 12-point deduction for the season after entering into a CVA - which is classed as an insolvency event by the EFL - to try to clear some of their debts.
Bury saw a winding-up petition against them dismissed by the High Court on 31 July, while Dale claimed the EFL were "working against" the club, to which Jevans later said that the league was "not standing in the way" of the club's survival.
The EFL had previously issued the club with a withdrawal of membership notice - which was itself suspended since 25 July - but this has now been lifted.
Bury have also previously been referred to an independent disciplinary panel after their opening-day fixture against MK Dons was suspended.
The summer of turmoil has also decimated the squad, with five former Shakers players going on to join Plymouth Argyle alone.
In Devon, the quintet have been reunited with manager Ryan Lowe, assistant Steven Schumacher and other backroom staff who both left Gigg Lane in June.