Arsenal are continuing to monitor Karim Benzema’s situation at Real Madrid and they have not ruled out making a bid for the striker towards the end of the transfer window, despite Rafael Benítez saying the Frenchman will remain at the Bernabéu.

Benzema is currently injured and he is not part of the Real squad at the four-team Audi Cup here in Munich. The 27-year-old hurt his thigh in training on Monday and there are doubts as to whether he will be fit for the start of the Spanish league season on 23 August.

The forward’s starting prospects under Benítez, though, are unclear, with the new Real manager having promised Gareth Bale a run in the team in a central striking position alongside Cristiano Ronaldo, who is also injured at present and not at the Audi Cup.

Benítez started Bale alongside Jesé in a 4-4-2 formation in Tuesday’s 2-0 win over Tottenham Hotspur, with the Wales forward scoring the second goal against his former club. Afterwards, Bale made it clear he considered the central role to be his favourite and most effective role.

Arsène Wenger, the Arsenal manager, has sought to cool the speculation regarding his interest in Benzema but he has said he is ready to take advantage of any opportunity that may arise on the market, much as he did on deadline day in September 2013, when he signed Mesut Özil from Real for £42.5m.

Real are not looking to push Benzema out of the door as they have done previously with other players, including Özil, and Benítez, when asked earlier in the week about the situation, said he thought “Benzema is going to stay with us. I’m very happy with him. There’s no reason to think that he’s going to go.”

Real, though, could be swayed by a massive offer from Arsenal. It should be noted, as well, that Benzema always dreamed of playing for Real and he would not consider a move away lightly.

Much will rest on whether Benzema starts Real’s two fixtures before the 1 September transfer deadline or he finds himself as the odd man out. Wenger has options up front, including Theo Walcott, Olivier Giroud and Danny Welbeck but Benzema would surely represent an upgrade.