Bury have rejected a Rangers approach for the Lancashire club so the Scottish club can play in England's League One at Ibrox.
Charles Green's consortium, who recently bought the debt-ridden club for £5.5m, proposed to purchase the Greater Manchester club.
The plan would alllow Rangers to take up Bury's fixtures for the upcoming season whilst still playing their home games at Rangers' current home Ibrox.
A source told the Sun: "Yes, Rangers really are thinking about this.
"They are in a position at the moment where they have no idea what the future holds. Acquiring an English club would get them the foothold they have always wanted down south."
Bury FC were quick to dismiss the claims the team would in effect move 200 miles across the border.
The club said: "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.
"Bury FC is a proud historical club and, as such, proudly represents the town, community, people and, above all, supporters of Bury.
"The directors of Bury FC place the integrity and morality of the club, and football as a whole, way above and beyond any possible financial gain and, as such, wish to reassure all Shakers fans of this fact."
The Football League said: "There has been no application to move the club. Any application would be treated under the regulations."
Even if the deal to buy the League One club does not seem likely, it is still uncertain where the Scottish club will be playing next season.
Green will discover on 4 July if the other Scottish premier league teams will allow a new team, which will be called TheRangers Football Club, to compete in the top division.
There are reports suggesting the Scottish Football League will compromise with the 54-times Scottish champions which would allow them to play in the Irn-Bru First Division
Green completed his £5.5m newco acquisition of the troubles club after his Company Voluntary Arrangement was rejected by the taxman.