The Los Blancos striker is still going strong in Spain but is being encouraged to end his career back in France.
Lyon sporting director Juninho wants Real Madrid forward Karim Benzema to finish his career at the Ligue 1 club.
Benzema, 31, came through the Lyon academy and starred in Ligue 1 before joining Madrid for €35 million ($38m) in July 2009.
The Frenchman has scored 233 goals for Madrid, helping the Spanish giants win two La Liga titles and four Champions Leagues among numerous other trophies.
Juninho, who played alongside Benzema at Lyon, is desperate for the forward to return to the club and has already floated the idea by him.
“My desire is to propose to Karim that he finishes his career at Lyon,” the Brazilian told OLTV. “He is from here, he feels from here. Why not make an economic effort between both parties to make it happen?
“We can’t offer the same salary as Real Madrid, but we will wait for the right moment.
“We exchanged messages when I was in Brazil. I felt like he would like to come. He has a lot of respect for the club.
“I want him to come and play with us for two years, and then train some of the younger players. Karim could be the leader that we need. I dream that he will end his career here at Lyon, his home.”
Benzema has made a fine start to this season, scoring 11 goals in 15 games in all competitions for Madrid.
His recent good form left Real coach Zinedine Zidane confused as to why he wasn’t called up by the France national team.
“He’s always wanted to play for the French side,” Zidane told a news conference. “To be honest, I don’t know exactly what’s going on.
“But from a football point of view, he’s the best. I think he should definitely have a place in the French national team. It’s beyond my role here, but he should definitely be called up.”
Lyon, meanwhile, are struggling in 14th in Ligue 1, with Rudi Garcia replacing Sylvinho at the helm last month.
Garcia’s side slumped to a 2-1 loss to Marseille last time out and will next face Nice after the international break.
Lyon finished third in the league last season but already have some serious catching up to do after just 13 games.