The Frenchman has been linked with a transfer away from the Ligue 1 side having fallen out of favour under manager Didier Deschamps.
Premier League rivals Fulham were also heavily linked with a move for the 26-year-old, who is reported to have been offered to the Toffees.
However, Gignac snubbed the chance of moving to England, opting instead to remain at the Stade Velodrome, with offers thought to have come in from Nice, Brest and Lorient for the former Toulouse star.
"Everton is a top club in England but for me Marseille is bigger and more attractive," Gignac said.
"I want to play one day abroad but at a bigger club like the Manchester Uniteds of this world.
"I do want to make a name for myself at Marseille. I love the club."
Everton ended up signing former Rangers star Nikica Jelavic ahead of Tuesday’s transfer deadline on a four-and-a-half year deal.
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