Vardy, who has been in impressive form in the Conference this season, scored Fleetwood's goal in their 5-1 FA Cup loss to the Seasiders at the weekend.
Within hours of that match finishing, Blackpool boss Ian Holloway had lodged an offer for the 18-goal centre-forward.
"I did receive a text from Blackpool on Saturday night, which was a long way short of our valuation of the player," Town chairman Andy Pilley told the Blackpool Gazette. "A lot of clubs have made contact and there has been lots and lots of interest in Jamie. Blackpool's is not the first bid and is not the best we've had.
"The size of the fee is for the clubs to negotiate but we value Jamie highly.
"Until we receive an offer which is attractive to us, Jamie will remain a Fleetwood player."
It is believed that Blackpool's bid was in the region of £750,000.