League One's bottom club, facing relegation if they lose at Oldham this weekend, say they need £1million to stay in business long-term.
An appeal for cash led to talks on Thursday, and a further statement from the board of directors on Friday confirmed the possibility of investment from "genuine Bury supporters".
It read: "As we did on Thursday, we have had another series of 'positive' meetings with potential investors into the football club on Friday.
"We can also confirm that the potential investors are also genuine Bury supporters and are as committed to the long term future of the club as the board of directors are.
"Although discussions are still at an early stage, the board of directors are feeling positive that these discussions will bear some fruit towards the long-term future of this football club."