The striker scored 66 goals for the Ligue 1 club across four seasons before his big-money move to the Spanish capital.
Benzema moved to Madrid in the summer of 2009 in a worth a reported €41m and he has made 513 appearances for the club since, netting 249 goals.
“It is a dream of everyone at this club to make him come back for two seasons and play in the Champions League with us,” sporting director Juninho told Radio Montecarlo, via Marca.
“He would be our leader and in addition to scoring goals he would give us the experience we need to win games.”
Benzema, who celebrated his 32nd birthday in December, has been in a rich vein of form over the course of the past two seasons – he netted 30 goals in total in the 2018/19 season before hitting 27 times last term.
Of Algerian descent, the frontman has emerged as the most important and in-form player for Madrid since the sale of Cristiano Ronaldo to Juventus in the summer of 2018.
His significance to the current team under Zinedine Zidane is demonstrated by his ever presence in attack and being favoured ahead of recent signings such as Luka Jovic and Mariano Diaz.