However, the Rao family, who own Rovers, have insisted that keeping hold of Rhodes is fundamental to their objective of achieving promotion to the top flight this season.
"We have recently received two official bids for the services of Jordan Rhodes from Hull City FC, both have been respectfully and categorically rejected. The owners of Blackburn Rovers wish to reassure fans that their intention is not to sell Jordan Rhodes as they, along with the manager and board of directors, feel that he is integral to our bid to gain promotion back to the Premier League," read a statement on the club's official website.
"Despite the necessity to comply with and address the pending restrictions of FFP regulations, the owners feel it would be a detrimental step to lose our top goalscorer and such an icon of this football club. We made our intentions clear this summer when we rewarded Jordan with a new and improved contract and we stand by that.
"We want to give Gary Bowyer and the team the best possible opportunity to get back to the top flight and Jordan has been and remains a significant part of that aim. It is also important to acknowledge that Jordan has acted, unsurprisingly, in a totally professional manner during this period of speculation."
Recent speculation had claimed that Hull's bid for the 24-year-old was worth around £12m.