Benzema faces an uncertain future at Real Madrid amid speculation Bernabeu bigwig Florentino Perez is chasing a new target man.
According to Don Balon, the France international has received an offer from Chelsea and is open to the idea of heading to Stamford Bridge.
Roman Abramovich is spearheading the Premier League club’s approach, the Spanish publication claim, and plans to spend big to secure Benzema’s signature.
Chelsea are set for one of the most important summers in their recent history.
Antonio Conte is expected to be given the boot and a host of first-team players could be dumped.
Up to nine stars face being moved on in the transfer window, with Abramovich set to take a more hands-on role in running the club.
Don Balon say a new striker is high on Abramovich’s wish list.
Alvaro Morata has flopped since joining from Real Madrid last summer, Olivier Giroud has one season left on his contract while Michy Batshuayi could seal a permanent exit after joining Borussia Dortmund on loan.
Benzema is reportedly the man Abramovich hopes to bring in to strengthen the attack.
The 30-year-old is aware that Real Madrid chiefs are looking to upgrade this summer and offers are beginning to trickle in.
But Abramovich would have to break the club’s contract rules to bring Benzema to Stamford Bridge.
Chelsea are reluctant to offer any more than 12-month deals to players aged 30 or over.
Benzema has struggled in front of goal this season, scoring just four times in 23 league appearances.
He has, however, contributed 10 assists and remains a regular name on Zinedine Zidane’s team sheet.