Barton has since issued an apology for his "transsexual" jibes at Silva and Baup has said that Barton's off-field actions are not his concern.
"Barton holds an important place in the team," BBC Sport quotes Baup as saying.
"I make decisions in the game - for example, that he did not start against Nice [last weekend]. That is my responsibility. Beyond that, it does not concern me."
Marseille host Bordeaux on Friday night in Ligue 1.