The Premier League giants are targeting the France international, should he fall down the pecking order.
Zinedine Zidane’s Real side are widely expected to make big money offers for either Borussia Dortmund forward Pierre-Emerick Aubameyang or Bayern Munich front man Robert Lewandowski in the upcoming close season.
A signing of such magnitude is expected to cost the Liga giants around £70 million and would force France international Benzema further down the Santiago Bernabeu pecking order.
The 28-year-old has enjoyed the most prolific season of his professional career this term, netting 22 goals in 23 league appearances for Los Blancos in a campaign fragmented due to varying injury problems.
According to the Daily Mail, Arsenal are prepared to enter the race for the complete centre forward in a bid to strengthen their options in the final third.
The north Londoners have not been put off trying to persuade Benzema to move to the Emirates Stadium despite last season’s embarrassing episode whereby the striker ruled himself out of a move to the Gunners on social media.
Benzema posted a picture of himself in the Madrid dressing room in August last year, captioning the picture: "Here this is my home!"