However, France head coach Didier Deschamps has moved quickly to play down the reports.
The 25-year-old centre-back played all 120 minutes of Arsenal's 4-3 penalty shootout defeat having entered the match already managing the injury, which had forced him out of the squad for the final Premier League fixture of the season at Crystal Palace and kept him away from training in the build-up to that game.
Foot Mercato reports that Saliba could be sidelined for several weeks and that the French Football Federation is genuinely concerned about whether he will be fit enough to feature when France open their World Cup campaign.
Deschamps addressed the reports directly when asked about Saliba at a press conference on Monday.
"He's here, everything's fine," the France head coach said. When pressed on reports suggesting the defender could miss the tournament, he was dismissive.
"That's not factual. I don't know where that came from and I don't want to know."
France are in Group D alongside Senegal, the Netherlands and Uzbekistan, with their opening fixture on June 16. How long Saliba's back requires for full recovery will determine whether Deschamps can rely on him from the start or must look to alternatives in central defence for the opening stages.