The Express claim boss Arsene Wenger is lining up a stunning move for the 20-year-old, who is said to have a release clause worth around £75m.
Madrid are hopeful of hanging on to the Spain U21 international, having already batted away advances from PSG and Inter Milan.
But the Gunners have also emerged as a possible destination with Asensio keen to ensure he’ll play first-team football during the coming season.
Footage from his incredible breakout year last season shows what a talent the former Mallorca man is.
Playing in a free role in the final third of the pitch, Asensio has scored some unbelievable strikes with eye-catching frequency – including two against Barcelona earlier this month in the Spanish Super Cup.
However, Arsenal fans met news of the potential switch with scepticism, as one wrote on Twitter: “I doubt this is true, but if it is I would happily take him at Arsenal.”
“A slight chance Arsenal would meet the clause – but wake up, he wouldn't want to sign for Arsenal. Go for realistic targets,” added a third.
Another chipped in: “Nothing is impossible in life but I see this as a very difficult mission.
“For now Madrid will not let him go because he's their future prospect.”
It comes amid reports that the club are willing to offload centre-back Shkodran Mustafi to Inter Milan in a deal worth £35m.
