Goal.com reported earlier on Thursday that David Moyes’ side were hoping to beat Tottenham to the £9 million signing of the 27-year-old Sevilla and Spain striker.
The agent confirmed talks had taken place but then ruled out a deal being completed before the deadline arrived at 11pm on Thursday.
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He believes the fee being discussed would not be enough to tempt Sevilla to sell before the summer, even if they do need to generate funds through player sales.
“It is impossible,” representative Juanma Lopez told the Liverpool Echo.
"Negredo is an important player for Sevilla and I am absolutely sure nothing will be done in this window.
"I know they have spoken to Everton but there is no way it will happen. Unfortunately there is no chance because Sevilla simply don't want to lose him, and if they do they will ask for crazy money.
"They are playing an important game [against Atletico Madrid in the Copa del Rey] and they want to do a lot in that competition. Negredo is important for that."
The Toffees may now turn to other targets, having already seen a move for FC Twente midfielder Leroy Fer break down due to a knee injury.