Mourinho was sacked by Man Utd in December following a 3-1 defeat to bitter rivals Liverpool, leaving the club's top-four prospects looking bleak.
For a while he looked set to secure a return to Real Madrid, flirting with them at almost every given opportunity during a series of media appearances.
But after Madrid opted to re-hire Zinedine Zidane following the sacking of Santiago Solari, Mourinho is having to reassess his options.
French publication L'Equipe linked him with Lyon on Wednesday, and the incumbent Genesio – whose contract expires at the end of the season – was welcoming of such speculation.
"We can only respect Mourinho," he told reporters. "He's a coach who has won everywhere he's been.
"He is maybe not the one I identify with personality wise, but I respect him a lot regarding his records and achievements in football. He's won everything.
"Everywhere he's been he's won a trophy. He's won Champions Leagues. Obviously, he's a great coach, so, if he succeeds me it would be an honour."
Midfielder Lucas Tousart was more reserved on the matter, though he does rate Mourinho among the world's best coaches.
"It is not something that we are listening to," he added. "A lot of things are 'revealed' and then appear at the end to be wrong, but I don't know. We'll see what happens.
"He was, and I think he still is, a great head coach. He accomplished great things in the biggest clubs.
"His last experience [at Man Utd] went badly. I don't know him personally, so there's not a lot I can say about him, but it's true that he's currently among the best coaches.
"He's among the ones who have done amazing stuff with their clubs."