According to Vital Rangers, the English playmaker is in Glasgow to complete a medical ahead of a transfer to the Ibrox giants this month.
The report claims that it remains unclear as to how much the club are set to pay for the Canaries gem, who is out of contract at the end of the season.
When asked if Cantwell and Tom Davies are among the players on his wishlist for January, Gers boss Michael Beale said:
“No names but I think they are both good players to be fair. Todd was an excellent player when he was young and playing against my Liverpool Under 23s.
“I thought he would go on and have a fantastic career. He had that at the start and he is maybe just looking for a move to re-ingite it but I think he is a fantastic player at a good age.”
Signing Cantwell on a permanent deal this month would be a dream first signing in charge of the Light Blues for Beale as he has the potential to be a terrific addition to the squad.
The midfielder, who was valued at £30m as recently as 2020, is in need of a fresh start after falling out of favour at Norwich and could reignite his career by making the switch to Ibrox.
He has not scored or assisted a single goal in nine Championship starts this term, after also failing to do so in eight starts on loan at Bournemouth last season, but his underlying data has been promising.
This also all comes after he enjoyed a terrific 2020/21 campaign in the Championship for Norwich as he averaged a Sofascore rating of 7.17 and produced six goals and six assists in 30 starts, having scored six times in the Premier League the previous year.
These statistics suggest that the former England under-21 international has the quality to deliver goals and assists from midfield for the Gers if Beale can help the 24-year-old to get back to his best in front of goal.
At the age of 24, Cantwell still has plenty of time left on his hands to get his career back on track and show that he can be a £30m-rated talent again.
If he can do that, by performing week-in-week-out for the Gers, then he will prove to be a sensational signing by Ross Wilson and a dream first addition for Beale.