Benzema was nurtured in Lyon’s academy and won four league titles with the club before departing for Real Madrid in 2009.
The 33-year-old has become a mainstay in the Real Madrid set up for well over a decade, helping Los Blancos to two league titles and four UEFA Champions League trophies.
Juninho returned to Lyon at the start of this season to become the club’s sporting director but has endured a testing start to the season.
Lyon lie 14th on the French Ligue 1 table after 13 matchdays and have already made one managerial alteration with Rudi Garcia replacing Sylvinho last month.
Juninho played with Benzema during the striker’s first spell at the club, and the Brazilian would love to have his former teammate make a return to his roots.
"My desire is to propose to Karim that he finishes his career at Lyon," Juninho 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 scored 11 goals in 15 appearances for Real Madrid this season.
