Labrune has now revealed that Marseille have received offers for both of the players, but he has not named which clubs have bid for them.
“We have offers for several players,” the Marseille chairman told RMC, as translated by Get French Football News. “If we have an offer that we like, we will open the door.
“We have never had as many offers for as many players as we do now. Thauvin, Imbula and Payet have a lot of offers.”
Payet has been on the books of Marseille since 2013 and is a France international.
The former Lille star scored seven goals and created 134 chances in 36 Ligue 1 appearances in the recently concluded 2014-15 season.
The 28-year-old had a pass accuracy of 80% and a shot accuracy of 47%, and won three headers, 66 dribbles and 17 tackles.
Thauvin has also been on the books of Marseille since 2013 and has yet to make his debut for the France senior team.
The 22-year-old scored five goals and created 53 chances in 36 Ligue 1 matches in 2014-15, and had a pass accuracy of 77% and a shot accuracy of 34%.