Souttar is out of contract at Scottish Premiership side Hearts in the summer and has decided to move on in search of a new challenge.
It is suggested that Souttar would rather leave Hearts in this month’s transfer window than wait until the summer, and Rangers are keen to keep him in Scotland.
However, Souttar’s career ambitions mean that it is far from certain he will agree to join the Gers.
It is claimed that he is minded to head south of the border to play his football in England, rather than remain in Scotland.
Souttar’s interest in playing in England is a boost for Sheffield United, who are keen to add him to the ranks at Bramall Lane.
Blades boss Paul Heckingbottom wants to strengthen his side’s backline during this month’s transfer window, with 28 goals conceded in just 22 games in the Championship.
Rangers are claimed to be keener on signing Souttar without a fee, when his deal expires, something else which could boost Sheffield United if they are willing to offer Hearts a fee for him this month.