According to an official statement, a bid of 17 million, plus a further 3 million in incentives, was lodged in April following his double against Athletic Bilbao.
Both Sevilla and Negredo swiftly rejected the proposal, with the latter uninterested in a move to Upton Park and president Jose Maria del Nido insisting the striker will remain at the club.
"He has four years left on his contract," Del Nido told reporters. "He is at home here. He has scored a lot of goals and delighted us with his football.
"The summer will tell us in due course if he will still be with us, but if you ask my opinion I'd rather there were no bids.
"West Ham offered 17 million euros in cash, with 3 million more in incentives, but we do not value the offer and the player refused."