The English midfielder joined Les Phoceens on a season-long loan basis from Queens Park Rangers at the start of the current season.
Having made seven Ligue 1 appearances, Barton has done enough to impress officials at Marseille.
"We haven't started the discussions yet with QPR but he's a likeable lad and we want to keep him, although we have no guarantees," said Anigo. "We have very good relations with QPR and extending the loan could be on the cards.
"He likes it in Marseille, he loves this city, which breathes football. He has a good attitude. He's a good professional in his work and in his day to day commitment. A lot of French players should take their example from him."
Barton has scored one goal for the club from 12 outings in all competitions.