Labrune blamed changes in French tax law for the prospective loss of Gignac - who has scored 48 goals in 128 Ligue 1 appearances for Marseille - with Premier League clubs likely to be interested, according to the British media.
Arsenal and Newcastle United could be keen on the 28-year-old forward, who 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.
Labrune believes that kind of form will see Gignac leave when his contract expires at the end of the season.
"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.
"His agent is right to say that, with his current displays, he is more likely to get better offers," Labrune said.
"But he loves the city and the club, so we're going to talk."
