The Jambos wideman was linked with a move to Ibrox throughout the summer, but the speculation rumbled on right up until the final day of the window as both clubs failed to agree a deal for him.
Walker’s contract expires at the end of this season and Rangers may have believed they could get him for less than his £1million valuation as a result.
But Hearts reportedly refused to play ball at the numerous bids received and Walker is still their player until at least January.
Ian Cathro was manager at the beginning of the Walker to Rangers talk before Jon Daly took over on a temporary basis.
Now Levein is the permanent Hearts boss after moving down from his director of football role – and one of his first media lines has been about Walker.
According to the Jambos gaffer, promises were made to Walker that weren’t kept. Per planetradio.co.uk, Levein said: “I don’t want to go into too much detail but if I was Jamie I’d be a little bit disappointed that a lot of the promises that were made to him weren’t kept. And not from our club.
Is Levein then talking about Rangers? You’d have to assume so.
Walker still looks likely to leave Hearts when his contract expires next summer, but if Levein’s comments are true then it might not be Ibrox which is his next destination.