The defender is tied to a lengthy contract at the Emirates Stadium but is still often linked with a move away from the Gunners, with former club Barcelona known to be in the hunt to take him back.
Reports now claim that Real Madrid are also targeting a move as they look to replace Dani Carvajal, who has doubts over his fitness as he suffers from a heart condition.
Carvajal had just extended his contract until 2022, and although he is set to make a return at some point, Real are in the need for reinforcements at right-back and are said to be targeting Bellerin.
Real president Florentino Perez is supposedly a huge fan of the 22-year-old and would be willing to pay in the region of £35 million for his services.
Arsenal are again likely to rebuff all interest, but that will not stop Real from chancing their luck with a bid.