Mbappe had received treatment for a "small niggle" in his right ankle, picked up playing for Real Madrid last weekend.
"The coach (Didier Deschamps) wants me to play. I don't think there will be a major problem," Mbappe told reporters on Thursday.
Deschamps added: "It's not prohibitive; it depends more on his sensitivity regarding his ankle."
Mbappe said he was feeling "more relaxed" in his life, having fully settled into life in the Spanish capital since joining Real from Paris Saint-Germain last season.
"A career can have some slightly more complicated years, years where you have a little more hardship," he said.
"But in life, I think I've adapted well to Madrid. This isn't an attack on France, but it's true that I'm more relaxed there. In Madrid, the lifestyle is different. It's less hectic than in Paris.
"I've managed to score goals. But I think that, moreover, in my game I'm also in a good mood, even if I think I can still do better," he said.
Deschamps urged his players not to underestimate Azerbaijan.
"Certainly, they're not among the best European teams, but they're coming off a draw against Ukraine," said Deschamps.
"Seven of their players play for Qarabag," which has won its first two Champions League pool matches, added the France coach.
Les Bleus are top of their group with two wins from two so far in qualifying. They host Azerbaijan on Friday at PSG's Parc des Princes stadium before travelling to Iceland three days later.