Bury will apply for a place in the National League after a proposal to readmit them to League Two next season was rejected.
Local MP James Frith has also claimed there are still "active and credible" bidders for the stricken club.
The Shakers were expelled from League One in August after a last-ditch takeover bid collapsed.
Mayor of Greater Manchester Andy Burnham has also called on the Football Association to find a "fair" solution.
The English Football League's 71 member clubs turned down the proposal for readmittance to League Two at a meeting on Thursday.
Burnham, who leads the Greater Manchester Combined Authority, has passed an emergency resolution calling on the FA to intervene.
He has asked the FA for an outcome that "respects the club's proud history as twice winners of the FA Cup".
The Bury FC Rescue Board - also backed by local MPs and supporters' group Forever Bury - met earlier and Labour MP for Bury North, Frith, updated supporters on social media.
"It was agreed that we will enlist the support of the FA with national meetings with them in the next fortnight, and apply for National League football for the 2020-21 season," he said on Twitter.
"This effort builds on our success to agree new ownership with the current owner, our commitment to securing the ground and a club rebuild plan which we will present in the coming weeks.
"The active credible bidders remain active and credible and we've still all we need to get this done."
Bury were sold by former owner Stewart Day in December for £1, but new owner Steve Dale failed to clear their debts and players and staff went unpaid, with the club served a winding-up petition by HMRC before agreeing a company voluntary arrangement.
"The winding-up order is for the current owner to address but none of the above is prohibited by this," Frith wrote.
"Whilst there are no guarantees (liquidation remains a possible threat as it always has) there is faith in the process involving the FA."
Frith dismissed any immediate prospect of taking legal action to secure a return to the league, forming a "phoenix" club or the local council buying the debt on the club's Gigg Lane ground, despite Burnham's support.
He added: "We can confirm, though, that the ground is protected as an asset of community value and that the mayor of Greater Manchester today passed an emergency motion to support all of the above.
"Bury FC only dies if we walk away and we're not walking away."