According to The Mirror (Transfer live blog, 15:28, Thursday, January 11, 2018), Graeme Murty's Rangers are interested in signing Arfield this month.
The 29-year-old Canada international midfielder knows Scottish football pretty well, having started his professional club football career at Falkirk.
Rangers have been quite busy in the January transfer window, and have signed Jacob Murphy and Sean Goss on loan from Brighton and Hove Albion and Queens Park Rangers respectively.
Arfield is a very good midfielder who has proved himself in the Championship and in the Premier League in England.
The former Huddersfield Town midfielder has also been linked with three clubs in the English top flight.
Burnley manager Sean Dyche, though, has stated that he does not want to lose Arfield in the January transfer window.
Dyche told Sky Sports: “We've had talks with him. He's sat tight on an offer so we'll keep open minds, as will he I hope, to what comes next.
"I have been [keen for him to stay] for a long time. Scott knows where it all stands, he knows the club's situation and he's been a very good player for us and continues to be.”