According to L'Equipe, the France captain has put coach Didier Deschamps in 'a difficult position' by deciding not to report for international duty in the current international break.
Mbappe wasn't named in France's squad for their upcoming Nations League games against Israel and Belgium.
Although he isn't injured, Mbappe indicated that he needed rest as part of his recovery from a recent hamstring injury.
However, the forward still featured for Real Madrid at the weekend as he played 71 minutes in a 2-0 win against Villarreal.
France star Ky;ian Mbappe is said to be 'damaging his image' with the national team
Deschamps is said to have been left annoyed by Mbappe's involvement in that fixture.
The France boss had agreed with Mbappe that he could be left out of the national team squad as part of his recovery.
Patrice Evra claimed that France are being more cautious with Mbappe now that he plays for Real Madrid rather than Paris Saint-Germain.
Former France defender Evra suggested that Les Bleus don't want to ruin their relationship with Real Madrid president Florentino Perez.
Speaking on Jeremy Rothen's s'enflamme podcast, Evra said: 'If you call him up and he gets injured, you damage your relationship with Perez.
'Real Madrid aren't PSG. You can't afford to take that kind of risk. But honestly, you're the ones who've built up this legend around Mbappe.
'With all due respect to him, he's not on Benzema's level. He doesn't even reach Benzema's ankle right now.'
Mbappe, who starred as France won the World Cup in 2018, has scored 48 goals in 86 caps for his country.
He is the the third highest scorer for France of all time behind Olivier Giroud (57 goals) and Thierry Henry (51 goals).