The defender is out of contract at Hearts in the summer and has decided he will not sign a fresh deal in order to look for a new challenge.
Rangers want to snap Souttar up, though it has been suggested he is keen on a challenge south of the border, where Sheffield United have admitted they are keen on him.
No side have yet to win the race for Souttar and it is suggested the battle for his signature is ongoing, with Rangers and Sheffield United prominent in the fight.
Souttar is suggested to prefer a move this month rather than waiting to see out his contract at Hearts.
The 25-year-old has turned out in 22 games across all competitions for Hearts this season, picking up three yellow cards in the process.
He is closing in on making 200 appearances in the Scottish Premiership, a total he would be likely to reach if he picks Rangers over Sheffield United.
It remains to be seen what other options Souttar might have on his table as he considers his next move.