The Hearts centre-back agreed a pre-contract last week to join in the summer.
“Rangers might try and bring the move forward by agreeing a fee this window,” he wrote in his Daily Mail column. “There are clear benefits to that for them – and for Souttar – but so much of it depends on Hearts and what they might demand to make it happen.
“You’d also think it could be wise for Rangers to leave Souttar where he is until after Hearts play Celtic.
“Their perfect outcome would be for the player to leave Tynecastle on a high, having helped takes the points away from Celtic in the title race.
“If he stays, then Hearts come to Ibrox on February 6. Souttar would be the centre of attention that afternoon.”