Ex-Lyon boss Garde has been heavily linked with the managerial vacancy at Villa Park but is reportedly keen to take with him two members of his old backroom staff.
Those coaches, Bruno Genesio and Gerald Baticle, are still working at Lyon and the Ligue 1 club have said they will not be allowed to leave.
Lyon president Jean-Michel Aulas told Le Progres: "Remi, I hope, will go to Aston Villa, he deserves a big English club.
"But an assistant under contract cannot leave
And anyway, a deputy cannot ask that."
Villa are searching for their third manager in eight months after sacking Tim Sherwood on Sunday.
Sherwood paid the price for a poor start to the season in which Villa won just one of their opening 10 Barclays Premier League games.
They are bottom of the table and four points from the safety line ahead of Monday's trip to Tottenham.
Garde, a former Arsenal midfielder, has emerged as the front-runner for the position this week.
The initial favourites, David Moyes and Brendan Rodgers, have drifted in the betting while there does not appear to have been significant movement concerning another potential candidate, former Leicester boss Nigel Pearson in recent days.
Former Sunderland manager Gus Poyet is now out of the reckoning having agreed to take over at AEK Athens.
Captain Micah Richards admits the next manager, whoever it is, must make an instant impact to turn around the club's season.
Richards told Sky Sports News: "The manager who comes in needs to be able to get us going straight away.
"We haven't got any time to settle in or blend in
We need to get going from the start
Whoever it is, whether it is Garde, lets hope they can do that.
"If they speak French obviously it is going to be easier for them (the French players) to understand how they want to play
Let's hope he speaks just as good English as French because we're in England
When I went to Fiorentina I had to learn Italian and I had to try to adapt."
Source : PA