The Gunners were touted as making a bid for the Spanish star, who is priced at £16.8 million.
According to Marca, Manchester City are now looking at Grimaldo to cover the loss of Oleksandr Zinchenko, who signed for Arsenal.
City were hoping to secure Marc Cucurella from Brighton and Hove Albion.
However, the two clubs are struggling to negotiate a fee, as Brighton value him much higher than City do.
The source states that if Brighton do not budge on their asking price, City will turn to Grimaldo instead.