Didier Deschamps believes Jose Mourinho could be tempted to join a French team at some stage in the future.
Having won domestic titles in Portugal, England, Italy and Spain already in his coaching career, Manchester United's manager has recently been linked with big-spending Paris Saint-Germain.
The Ligue 1 side have the financial muscle to tempt Mourinho, but current PSG boss Unai Emery has yet to taste defeat this season and has already steered the club through to the knockout stages of the Champions League.
France national team boss Deschamps told a media conference: "I know you talk about a lot of things in England. If Jose Mourinho wants to come, why not?"
"I think he is pretty happy at Manchester United at the moment. He used to visit a lot of countries. He visited Italy, Spain, England. Not France yet. Why not?"
Deschamps recalled United's Anthony Martial to a 24-man squad for the upcoming friendlies with Wales and Germany — but fellow forward Karim Benzema was again left out.
The Real Madrid striker, who has scored just two goals in 12 appearances for his club this season, has not featured for France since October 2015 after becoming embroiled in a scandal involving an alleged attempt to blackmail international colleague Mathieu Valbuena.
"I'm here, I have two games to prepare for. I've called 24 players, and I trust them," a defiant Deschamps said when questioned over Benzema's continued absence.
"It doesn't annoy me [the debates about Benzema]. It's part of the media landscape. You are free to do whatever you want, whenever you want. It's not something that will change my mind or change my ideas about the French team."