HITC Sport understands that the free agent midfielder is to speak with the Championship club in the next 24 hours.
The midfielder is expected to meet with the Championship club in the next 24 hours as he continues in his bid to find a new club.
Barton has been a free agent since reaching the end of his contract at Queens Park Rangers and being released following their relegation out of the Premier League.
Several clubs across the top two tiers of English football have been linked with a move for the former Manchester City and Newcastle United man.
Nottingham Forest and West Ham United are reported to have led that hunt, but no agreement has been reached and Barton remains up for grabs.
That has kept the door open for Burnley, with the Clarets now preparing to firm up their interest.
The Clarets tumbled out of the top-flight last season alongside QPR, but intend to bounce back at the first time of asking.
Bringing in a player of Barton’s experience and undoubted ability would certainly aid them in that quest, but there is plenty to discuss – including the role he would play at Turf Moor and salary demands – before any deal can be struck.