The legendary forward only ended his long-term association with Real Madrid during the summer in order to make the lucrative switch to Al-Ittihad.
However, while the 36-year-old has chipped in with 12 goals from 20 appearances in all competitions, his club sit 25 points adrift of leaders Al-Hilal in the Saudi Pro League.
Reports have also indicated that there are issues behind the scenes, with Benzema said to have missed a number of training sessions and having not participated in the mid-season training camp in Dubai.
As a result, there has been widespread speculation regarding a transfer elsewhere, despite the veteran being on a lucrative three-year contract with the defending Saudi Arabian champions.
Arsenal and Chelsea have each been credited with an interest in negotiating a loan deal for the Frenchman as they bid to strengthen their respective attacks.
Mikel Arteta is looking for a proven central forward with only eight Premier League strikes having come from Gabriel Jesus and Eddie Nketiah this campaign, while Nicolas Jackson and Armando Broja have each been inconsistent for Chelsea.
Nevertheless, according to The Guardian, Lyon are contemplating whether to try to pull off what would be regarded as one of the transfers of the January window.
Benzema came through the academy system at Lyon before ultimately making his name in the first team, scoring 66 goals from 148 appearances and winning seven pieces of silverware, including four Ligue 1 titles.
Times have now changed with Lyon battling to avoid relegation, Les Gones currently sitting in 16th spot in the standings and just four points above bottom position.
Compromises would
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