HITC Spors understands The Gers have made contact with Hamitlon
The 25-year-old is seen as one of the hottest prospects in the Scottish top-flight and a host of English clubs have been checking on his progress in recent months.
Like Rangers, Celtic have also been keeping close tabs on him - but their city-rivals have now made a move as they look at a possible deal for the midfielder.
Hamilton Academical manager Martin Canning
Crawford has spent his entire career with The Accies, and last month their boss Martin Canning emphasised his desire to try and keep hold of Crawford until the summer.
With youngster Ronan Hughes also attracting interest, Hamilton now look as if they will lose one of them and Rangers are hoping they can tie up a deal for Crawford.
Gers boss Mark Warburton has a limited budget at Ibrox, but Crawford is clearly seen as a top target.
Crawford, whose current deal runs until 2018, is widely tipped to win a full Scottish cap in the coming months.
Hamilton Academical's Ali Crawford in action against Celtic