The Spaniard is reportedly being lined up by the Premier League champions this summer, as Pep Guardiola looks to finally solve his side's problems in the left-back area.
Numerous injuries and criminal investigations into Benjamin Mendy saw the Frenchman unavailable for City during much of the 2021-22 campaign once more, which led to Joao Cancelo and Oleksandr Zinchenko filling in for much of the season yet again.
Guardiola is therefore keen to bring in a natural left-back during the current transfer window, with Cucurella being identified as the primary target.
Despite talks of City accelerating their efforts to sign the Spaniard, Brighton's chairman has revealed that no bids have been lodged for the 23-year-old so far.
Speaking to The Argus, Bloom said: "All I can say about Marc is he is a tremendous player, a tremendous person. He is brilliant for the dressing room. The players love him.
"Graham (Potter) and the coaching staff love him, I love him, the fans love him. He was unbelievably good last season, his first season in the Premier League. We are hoping for more to come and we haven't had a bid for him."
However, Bloom did later admit that Brighton "have to be realistic" when it comes to Cucurella's future and hinted that should an acceptable offer arrive - believed to be in the region of £45m - then the Seagulls would not stand in the player's way.
The left-back enjoyed an impressive first season with Graham Potter's side in 2021-22, making 39 appearances across all competitions, and was voted the club's Player of the Year.