Souttar is wanted by a host of clubs in England with Sheffield United, Blackburn Rovers and Stoke City among those said to be interested in the Scotland centre-back.
The 25-year-old is free to sign a pre-contract with another club in January ahead of his current Hearts deal expiring in the summer.
And according to the Herald & Times, Rangers boss Giovanni van Bronckhorst wants to take the centre-half to Ibrox to bolster his defensive options with Connor Goldson and Leon Balogun out of contract at the end of the season.
Van Bronckhorst made his first acquisition of the January window on Wednesday as he snapped up midfielder James Sands on an 18-month loan deal from New York City.
Nathan Patterson’s £12million sale to Everton has raised funds for new signings as the Rangers boss looks to put his own stamp on the squad he inherited from Steven Gerrard.