Bury's application to join the National League system in 2020-21 has been rejected by the Football Association.
The Shakers lost their place in League One last season because of financial problems and the collapse of a last-ditch takeover bid.
Despite not having a league to play in, the club, founded in 1885, still exist.
The FA said the decision not to accept the application related to Bury's "financial resources, ownership and insolvency status".
"This decision was not taken lightly as both the FA and its Alliance Leagues Committee recognise the history and standing of Bury FC," an FA statement said.
"As a result, the Alliance Leagues Committee would welcome an application from the club to join the National League system for the 2021-22 season and detailed guidance has been provided in relation to the various conditions that would be expected before one could be considered."
The Shakers released a statement later on Friday saying they planned to resubmit an application for the 2021-22 campaign.
"In the future all these issues will be resolved and Bury FC will be back playing football at Gigg lane rest assured, our application for 2021-22 season is being prepared now and will be chased monthly to avoid a repeat of this atrocity.
"Let's hope because a further season has elapsed they don't try to place us in tier seven, as leaving League One we were supposed to get a high placing the following season as the demotion was the sentence."
Bury appeared to be on the brink of liquidation after their expulsion in August 2019 when another prospective buyer ended their interest two months later.
A winding-up petition served to the club over an unpaid tax bill was dismissed in February, giving the financially-troubled Shakers a reprieve.
Bury AFC, a club formed by fans of Bury FC, were allocated a place in the 10th-tier North West Counties League Division One North.
There had been doubt over the status of the new club after the non-league seasons at seventh-tier level and below were voided by the FA, but they have now been given a place for next season.