The 28-year-old forward - who has scored 48 goals in 128 Ligue 1 appearances for Marseille - has a contract until the end of the 2014-15 campaign and a number of Premier League clubs are supposedly keen on signing him.
Labrune has now blamed changes in French tax law for the prospective loss of Gignac and he believes the striker's fine form this term will see him leave in the summer of 2015.
"It's going to happen because employer contributions and taxes have gone through the roof in France," the media mogul told Le Journal de Dimanche.
"We would like to keep him but it seems to me utopian to think that he will lower his salary to stay with us."
Reports in the French media claimed last week that Gignac might be tempted to sign a new contract with Marseille due to their stunning start to the season - eight wins and a draw from 11 games - but Labrune remains unconvinced.
"He loves the city and the club, so we're going to talk.
"But his agent is right to say that, with his current displays, he is more likely to get better offers."
Gignac has hit the back of the net 10 times in 11 league matches this season as Marseille have stormed to the top of Ligue 1 under new coach Marcelo Bielsa.