While landing Nathan Ake from Bournemouth, City have been seeking a second centre-half signing this summer and their search led to Gimenez.
Cerezo confirmed: "Yes, we received an offer.
"However, Jimenez is a great footballer, and we need these in the team."
Spanish media sources say the offer tabled was €85m. Gimenez, 25, has a contract to 2023 at Atletico Madrid.