Ayew, 23, has expressed a desire to move away from the Stade Velodrome, with Liverpool his preferred destination.
Aside from loan spells at Arles and Lorient, the Ghana international winger has spent his entire career with Marseille, helping them to the Coupe de la Ligue title in 2011.
However, Ayew is reported to have clashed with manager Elie Baup over his desire to play as a central striker.
Baup is keen to retain the nucleus of the side that secured second place in Ligue 1 last term, but Labrune is willing to part company with Ayew.
"Ayew has informed me of his intentions," Labrune told Le Parisien.
"If an offer from a big club comes in and we like it, I will investigate it.
"But we’re not at that stage at all yet."
Ayew made 45 appearances for Marseille last season, scoring 12 goals.
'I’d probably pick Cole Palmer alongside Bellingham and Rice in there at the moment. For me, Declan Rice is good enough to play that central midfield role on his own' Thomas Tuchel advised to DROP Manchester City star by England legend
Manchester United staff threatened with sacking for leaked information... in a leaked email
