Lyon president Jean-Michel Aulas says Jose Mourinho turned them down because he has already found a new club.
Aulas had contacted the former Manchester United manager about the role after Sylvinho was dismissed from his position on Monday evening.
"We had some fairly flattering exchanges over SMS. It was nice for everyone. He did not accept our proposal to meet because he has already chosen another club," the Lyon chief admitted in a telephone press conference on Thursday morning, according to Get French Football.
Mourinho wants to find a job in England rather than moving to France, as his family are still based here following his time at Old Trafford and Chelsea.
Laurent Blanc is the other main target for Aulas and will be holding a meeting with the club over the coming days.