The French striker is reportedly considering retiring at the end of the season ahead of his 37th birthday on Thursday.
Benzema has already retired from international football having played his final match for France in 2022.
In 97 caps for Les Bleus, Benzema scored 37 goals and featured at four major tournaments.
His potential decision to hang up his boots may lead to a return to the Santiago Bernabeu after two years away.
According to Relevo, Benzema plans to head back to the Spanish capital once he retires.
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He is already said to be weighing up ending his playing career at the end of the season.
However, current club Al Ittihad are hoping Benzema will see out the remainder of his contract.
The deal which the 2022 Ballon d'Or winner signed upon his arrival last summer still has 18 months remaining.
By the time his contract expires, though, Benzema will be 38-years-old.
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Benzema has already reached an agreement with Real Madrid to become a club ambassador when he retires.
It comes after a stunning start to the campaign for Benzema, who has scored 10 goals in 10 league appearances this term.
Prior to moving to the Saudi Pro League, he spent 14 years with Los Blancos.
During that time, Benzema scored 354 goals in 648 appearances, making him the club's second all-time top scorer and fourth highest appearance maker.
Meanwhile, he won 25 trophies including five Champions Leagues and four La Liga titles.
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