The striker came through the academy at the Ligue 1 side, but left for the Bernabeu in July 2009 after impressing with the first team.
Benzema has scored 233 goals for Real Madrid since making the move, winning two league titles and four Champions Leagues.
But Juninho, a former Lyon team-mate of the forward, wants the 31-year-old to return to his hometown club before hanging up his boots.
"My desire is to propose to Karim that he finishes his career at Lyon," the Brazilian told OLTV (via AS).
"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."
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