The Gunners could face competition from Bayern Munich for the player, however.
The defender is currently frustrated with life in Spain, as he cannot break into the first team set-up at the Nou Camp.
Instead, he finds himself plying his trade in the Spanish third division with Barcelona B, after they were relegated from Spain’s Segunda Division last season.
That is not an ideal situation for the highly-rated youngster, who sees himself playing at a much higher level than the one he currently graces.
They will be boosted by the fact that the player’s contract is due to expire in the summer, and it looks unlikely that the club will exercise an option to extend it further.
The Gunners could be his first choice as well, with them having a strong history of developing La Masia graduates in the past, with Cesc Fabregas and more recently Hector Bellerin starring in their first-team.
However, while the player is keen for competitive football at the top level, it is believed Grimaldo would prefer to stay in Spain with Barca if they can guarantee a promotion to the senior ranks.