Gignac, 28, has enjoyed a productive campaign with 16 league goals despite what has been a largely disappointing Ligue 1 season for his side.
But the 17-time international believes he is little chance of representing France in Brazil, where they will face Switzerland, Ecuador and Honduras.
"I don't really any longer believe I can do it," Gignac was quoted as saying by the Ligue 1 website.
"There are a number of players who have also had a good season: Bafetimbi Gomis, (Alexandre) Lacazette and (Kevin) Gameiro.
"I had said that I would force (France coach Didier) Deschamps to take me, I did what I had to do, I have had a good season, but it's not enough.
"I was picked in September and I played 30 minutes against Georgia, but I didn't make an impact. I was a bit timid, which isn't like me at all. And since then, nothing."
France's 0-0 draw in Georgia in September last year was Gignac's most recent appearance for the national team, coming on for Karim Benzema but failing to impress.
Gignac's form has seen him linked with a move away from Marseille, but he is likely to stay at the club and play under Marcelo Bielsa.
"It's most likely that I will stay at OM, but will I extend my contract or not? We're going to talk about that at the end of the season," he said.
"I want to discover the Bielsa method. I have a good chance of getting along with him as they say he has character, and I'm not lacking that.
"The method and the demands he puts on players that are being written about in the papers don't scare me. It is, after all, our job to work to the max."
