According to an official statement, a bid of £14.5m [€17m], plus a further £2m [€3m] in incentives, was lodged in April following a double against Athletic Bilbao.
Both Sevilla and Negredo swiftly rejected the proposal, with the latter uninterested in a move to Upton Park, with 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 €17m in cash, with €3m more in incentives, but we do not value the offer and the player refused."More recently, West Ham have had a £15m bid for Andy Carroll accepted following a season-long loan spell.
Goal exclusively revealed, however, that Carroll is prepared to accept a bit-part role at Liverpool in favour of joining Sam Allardyce's side on a permanent basis.