Benzema, 31, came through the Lyon academy and starred in Ligue 1 before joining Madrid for €35million in July 2009.
The Frenchman has scored 233 goals for Madrid, helping the Spanish giants win two LaLiga titles and four Champions Leagues among numerous other trophies.
Juninho, who played alongside Benzema at Lyon, wants the forward to return to the club.
"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.
Lyon, meanwhile, are struggling in 14th in Ligue 1, with Rudi Garcia replacing Sylvinho at the helm last month.