The QPR midfielder spent last season on loan at the Stade Velodrome as les Phoceens finished second in Ligue 1 and qualified for the Champions League in the process.
Barton, who enjoyed a season-long loan spell with the Ligue 1 club, remains contracted to the Loftus Road outfit and Baup is unsure if the midfielder will head back to France - though is keen to sign Barton on a permanent basis.
"Joey Barton's comeback? I do not know how it will evolve," he told L'Equipe. "The club and the player agreed about the challenge ahead, but he still belongs to QPR."
Barton himself has spoken of his desire to return to Marseille following a stint that saw him make 28 starts in all competitions in France, scoring once.
The former Newcastle United and Manchester City player, 30, still has two years left on his current deal at Loftus Road.