It has been reported that Rangers are planning to make a move for the 28-year-old defensive midfielder before the window closes on Monday.
The report has added that Everton manager Carlo Ancelotti has told the Bosnia and Herzegovina international that he is not in his plans for this season.
Besic has been on the books of Everton since 2014 when he joined from Ferencvaros.
The 28-year-old defensive midfielder was expected to be a big success at Goodison Park, but he has failed to establish himself as a key figure in the team.
The Bosnia and Herzegovina international defensive midfielder was on loan at Middlesbrough during the second half of the 2017-18 season and for the 2018-19 campaign.
Besic was on loan at Sheffield United last season, with Blades manager Chris Wilder describing him as “an excellent all-round central midfielder” and “someone who can do everything we want a midfielder to do” on the club’s official website in August 2019.