The 30-year-old Barton was sent out on loan by the London club in disgrace this summer following his red card shame at former club Manchester City on the final day of last season, which brought him a 12-match ban.
But Barton has flourished in the south of France where, after being made to serve his ban and wait for a league debut, he has quickly become a key cog in a Marseille side in a three-way tie with Paris Saint-Germain and Lyon at the top of Ligue 1.
And Anigo insisted Barton's impact had come as no surprise to him.
"He was described as an animal, but he is just the opposite. He is funny, intelligent, and he fights for victory," Anigo told L'Equipe.
"We can see that the team has been lifted by his competitive spirit. He is now established as a leader in our group.
"He is very happy here, maybe he has found the right club for him. Should he desire (to stay) it could be very good. We have a very good relationship with his club QPR."