Arfield is a free agent in June and Rangers would be pulling off a coup by signing the Canadian.
They will also hope he lasts longer than the last player they signed from Burnley on a free transfer, Joey Barton.
Barton lasted just weeks into the season at Rangers in 2016/17 before his contract was terminated following a fall out with manager at the time Mark Warburton after a 5-1 loss to Celtic.
This was an incident Scott Arfield gave his view on at the time, and he was critical of Rangers' handling of the situation, suggesting they messed up.
He told the Daily Mail that Rangers created the problems with Barton rather than the other way around.
Speaking in March 2017 Arfield said: "I honestly think it was Rangers who created the problem. They didn't use him properly and that was the downfall. Joey's a massive character, a leader and a winner. Yeah, he can rattle a few cages. But those are the guys who can also inspire a full dressing room.”
“It seems to me like the Rangers players just couldn't hack him or didn't want to hear some home truths. Getting hammered 5-1 against your biggest rivals, it was never going to be rosy when they went into training on the Monday morning. It speaks volumes for Joey – and reflects really badly on Rangers – that he has come back down here and has started winning man-of-the-match awards straight away."
Now it would be a surprise if just a year after making these comments Arfield suddenly signed at Ibrox, but you can never say never in football.
Arfield is not known as a controversial character and would not likely create the same tensions as Barton did, so perhaps he is confident they could handle him, even if they struggled with Barton.