Rangers have new owners but it remains uncertain where they will play next season with Scottish Premier League clubs voting in July on whether to readmit the 54-times champions to their ranks after the side's parent company went into administration.
A separate report in the Daily Telegraph said Rangers could be excluded from the SPL but relegated just one tier to the first division as a compromise, rather than having to start from the bottom rung in the third division.
"Whilst investment into Bury Football Club is always welcome, any offer of investment will only be viewed at taking the club forward in its only one guise possible - based in the town of Bury, and as Bury Football Club," the club said in a statement on its website.
A club spokesman said there had been "no contact" with Rangers.
Bury won the English FA Cup twice early in the last century but have mainly played in the lower leagues in recent decades, overshadowed by Manchester's two big clubs, City and United.
