Joey Barton was at Murray Park on Saturday for talks with Rangers.
The gifted midfielder helped Burnley clinch the English Championship title this season but is out of contract.
Rangers are looking to strengthen their squad after winning promotion to the Scottish Premiership and are keen to add experience.
Barton, 33, has had a long and colourful career in which he has been no stranger to controversy. But his ability as a driving central midfielder has never been in doubt.
He began his career with Manchester City, playing over 130 league matches before moving on to Newcastle United, Queens Park Rangers, Marseille and then Burnley.
He was capped once for England, in 2007.
He played 38 league matches for Burnley this season as they clinched the title and sealed a return to the Premiership.
Rangers’ head of recruitment Frank McParland used to work for Burnley as sporting director and was employed by the Lancashire club when Barton signed.