Sean Dyche claims Barton's place among the training squad at Gawthorpe Hall is purely for fitness reasons and he is not currently part of the first team set up.
But priced at 1/3 for Burnley to be Barton's next club, it is looking likely that the midfielder will sign with Burnley for a second time.
Barton was part of the title winning team that won promotion to the Premier League in 2016 and was named in the PFA team of the year. The 34-year-old then joined Rangers where he was involved in a training ground bust up and found guilty of breaking betting rules before being let go.
Dyche has failed to commit on Barton's future but insists the emphasis is on 'getting himself fit'. Whether Barton is still able to compete in the English top flight is up for debate however.
Derby and Aston Villa, both priced at 7/2, are among the others rumoured to be interested in Barton. A move overseas to the MLS or China, priced at 25/1, could tempt Barton, who has previously played abroad with Marseille, while Birmingham remain outsiders, also at 25/1.