Chairman Brian Fenton revealed last month that the Shakers, relegated from League One at the end of the season, will go out of business unless they receive a cash injection of £1million.
And a statement from the club on Thursday claimed they are close to completing negotiations with investors and hope to have some "good news" to report soon.
"The board of directors at Bury FC can confirm that negotiations are ongoing and are approaching completion," read the statement.
"The board would further like to thank supporters for their patience and understanding whilst these talks continue.
"Under the terms of these discussions, we have been unable to make further comment, but as discussions approach the final stages we hope to be able to reveal good news for everyone involved with Bury Football Club in the very near future."
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