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.
There has long been speculation that Rangers and Glasgow rivals Celtic might seek a route into the lucrative English Premier League.
Bury, a town on the edge of English city Manchester, dismissed the report in The Sun newspaper saying they could be bought out and their home shifted 200 miles north to Glasgow.
"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.
Rangers have applied for readmission to the 12-team SPL but need the backing of seven other clubs to maintain their status.
The Telegraph report said an agreement was in the offing, with Rangers formally voted back in but then immediately demoted one level for past financial mismanagement.
Rangers were too strong on the pitch and had too many fans to be safely accommodated in the lowly third division, the report added.
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