The Frenchman has opted against a big-money move to England, having reportedly been on West Ham's transfer wishlist as they continue to struggle in the absence of Andy Carroll
The France international has scored eight goals in 17 Ligue 1 fixtures for Jose Anigo’s side this season, who sit in sixth place in the table.
Gignac was rumoured to be a January target for Premier League strugglers West Ham, as the Hammers continue to falter in the absence of the injured Andy Carroll, but the 28-year-old has no intention of moving to England.
"Without giving away any secrets, in the last few weeks he was subject to a fairly large offer from an English club, which he refused," Labrune told RMC.
"We are very happy to continue with him, at least until the end of the season.
"What interests me is what happens on the pitch, that he scores goals and helps us win games.
"We will look at financial considerations in due time."
The Frenchman joined Marseille from Toulouse for €16 million in August 2010, though he has failed to replicate his goal haul from the 2008-09 season, when he topped the goalscoring chart in Ligue 1 with 24 goals.