"We're not in a position where we used to be a few years ago, where if someone came knocking we had to sell. We don't have to sell."
Hull manager Phil Brown is understood to be a fan of both McCormack and Wales midfielder Joe Ledley, whose Cardiff contract expires at the end of this season.
"We've made our move, we've put a bid in for Ross McCormack but the bid has been rejected," Brown told the Hull Daily Mail.
"Hopefully we can agree terms between the two clubs and the player still, but we won't raise what we've bid because we think it's a good offer."
McCormack only signed a new four-year contract with the Bluebirds last month, but then said that he would like a move to a Premier League club.
However, he has this week insisted he is happy at Cardiff after distancing himself from a report accusing the club of pricing him out of a top-flight move.
"I'm happy and want to stay... I'm not planning to go anywhere," he said.
Hull are keen to add more firepower to their squad ahead of the start of the Barclays Premier League season on 15 August.
Hull completed their first summer signings on Thursday by bringing in midfielder Seyi Olofinjana from Stoke and Villarreal striker Jozy Altidore on loan.
Former Wigan striker Henri Camara is currently on trial with the Tigers while a bid for defender Habib Beye has been accepted by Newcastle.
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