The Scottish champions, who have just signed Aaron Ramsey on loan from Juventus, already have Souttar locked down on a pre-contract agreement.
He is due to arrive at Ibrox in the summer, but Rangers have tried to bring him in this month by agreeing a fee with Hearts.
However, they have had two bids rejected and despite contacting Hearts again today have not found common ground.
It is suggested that the two clubs are still some way apart on their respective views on a transfer fee.
With the clock now ticking down on the transfer window in Scotland, Rangers are doubtful that they will be able to sign Souttar.
The most likely scenario now sees the Hearts defender arriving in the summer as a free agent.
Souttar has made 25 appearances for Hearts over the course of this season so far, coming up against Rangers on two occasions.
