Former Manchester City and Newcastle United man Barton joined the Clarets in the summer after leaving Queens Park Rangers at the end of last season, and has been an important figure in Dyche's side.
The 33-year-old has made 27 appearances in all competitions for the club this season, scoring two goals, and his manager confirmed that he is one of a number of players being talked to about potential new contracts.
Dyche told the Lancashire Telegraph: "We always have lines of communication open with all of our players, [Barton] is just one of them."
Barton's current deal at Turf Moor is due to run out at the end of the season after he was signed for just a single year last summer.
His performances this season have gone some way to winning over those Clarets fans who were initially sceptical of his signing because of his disciplinary problems in the past.
The one-time England international, who has played over 250 Premier League games with City, Newcastle and QPR, has added experience and steel to the Burnley midfield.
Dyche's side are fighting for immediate promotion back to the top flight and are currently second in the Championship, one point off Hull City at the summit of the second tier.