The France international, who was not a part of his country’s final-reaching Euro 2016 squad, boasts 161 goals in 318 appearances for Los Blancos.
The 28-year-old featured for Zinedine Zidane’s side during a 3-2 defeat in the European Super Cup last week but his future at the Bernabeu remains open to speculation.
Cristiano Ronaldo is expected to be used as a central striker this season, throwing Benzema’s starting Xi spot into jeopardy.
Likewise, he now faces competition from summer signing Alvaro Morata, who returns to the Spanish capital after winning consecutive Serie A titles with Juventus.
Perhaps due to that uncertainty, Paddy Power are offering notably short odds on the 6 foot 2 striker completing a transfer to the Premier League.
They rate Arsenal’s chances at 3/1 – in other words, 25% – but put Manchester United as the firm front-runners with odds of 7/4.
That is despite United already signing one star striker in Zlatan Ibrahimovic, who scored on his Premier League debut against Bournemouth last Sunday.