Cantwell is tipped to depart Championship side Norwich City during this month’s transfer window and his deal at Carrow Road runs out in the summer.
The midfielder is holding talks with interested parties as he weighs up what would be the best next step in his career.
Cantwell has options on the table, but is claimed to favour a move to Ibrox to sign for Rangers.
The Gers have held positive talks with the midfielder and will be hoping they can push a deal over the line.
Rangers boss Michael Beale sees the benefits of bringing in Cantwell now and not waiting until the summer as it would give him time to adapt.
However, Rangers have not yet put in an official bid for the 24-year-old.
