West Ham co-chairman Sullivan
Vardy, who's in line to start for England at this summer's European Championship, fired the Foxes to an unexpected first ever Premier League title last season, with Sullivan's West Ham ending the campaign in seventh.
Despite this, the ambitious Hammers, who relocate to the Olympic Stadium this summer, were said to have tabled a shock bid for the 24-goal striker.
England man Vardy is believed to be Arsenal bound
And Sullivan confirmed via West Ham's website that the club had been keen on Vardy, however, with the Yorkshireman now en route to Arsenal, he conceded that a deal would not have been financially viable.
"It was reported that one of [West Ham's] targets was Jamie Vardy, and while it is true that we would loved to have had him, the numbers being talked about in a potential move to Arsenal show that the market is going potty," Sullivan said.
"It is safe to say that signing him would have smashed our current wage structure and we are determined to buy players with good value in this mad market."
Dimitri Payet is reportedly the Hammers' top earner, but Sullivan says Vardy would have earned more
He added: "We’re working 24 hours a day, seven days a week to make this happen, and with five bids in for players at the moment, we are hopeful that we can bring you some exciting news soon."
It has been widely reported that Arsenal have triggered a £20 million release clause in Vardy's contract, which was only applicable to Champions League clubs anyway.
Had West Ham pursued their interest, it is likely they would have had to pay far in excess of that amount to tempt Leicester into a sale.
Player of the season Vardy turns 30 in January