The forward suffered a muscle injury in September but made a successful comeback to the pitch in the Champions League match against French team Lille last week.
France coach Didier Deschamps left Mbappe out of the squad he announced on Oct 3, saying that the 25-year-old lacked preparation, having played too few matches.
It was agreed that he was declared not fit for international duty and would remain in Madrid to recover to full fitness.
But Mbappe started Real’s 2-0 Spanish La Liga win against Villarreal on Oct 5, which reportedly annoyed Deschamps.
“Either you’re injured, and you don’t play with your club and you’re not called up in the national team,” former France international Maxime Bossis told French sports daily L’Equipe on Oct 7.
“But when you come off the bench in the Champions League and you start a league game, it makes things fuzzy. He’s a special player. We’ve known that with Michel Platini, when we still wanted him with us when he was injured.”
Mbappe’s situation is more complicated because the former Paris Saint-Germain player is the national team captain after being handed the armband ahead of Antoine Griezmann, who last week announced his retirement from international football.
Griezmann’s commitment to Les Bleus was never in doubt as the Atletico Madrid forward played a record 84 consecutive matches for his country between 2017 and 2024.
“As a captain (Mbappe) must be an example for the fans, and he has not been,” Fabien Bonnet, spokesperson for the Irresistibles Francais, the main France supporters’ group, told L’Equipe.
“What emerges is that the real captain, Antoine Griezmann, is gone.”
Reports have said that Deschamps could look for a replacement captain.
Mbappe’s clubmate Aurelien Tchouameni is one of the options, as per reports from L’Equipe, on the back of a strong start to the season, alongside centre-back William Saliba.
France, second in Group A, face Israel in Budapest on Oct 10 and travel to Belgium on Oct 14.