"Yes, we have made an improved bid. It was rejected," Hughes revealed at a press conference to unveil City's first January transfer window signing Wayne Bridge.
"We still want to bring Roque Santa Cruz to the club if we can. But obviously he's Blackburn's player and they do not want to deal at the level we have made a bid at.
"I think we bid 12 million in the summer and it [the improved offer] was significantly higher than that."
Asked whether City would return with another offer, Hughes replied: "We'll have to wait and see."