Moyes had hoped to secure the signing of Fer before the kick-off of Wednesday night's 2-1 win over West Brom but the deal collapsed after they tried to renegotiate payment of the £8.6million deal with FC Twente when the player's medical identified an issue with a knee problem.
While Moyes was downbeat about his chances of bringing anyone else in place of Fer, the Toffees are understood to be interested in Negredo.
The 27-year-old Spain international, who has been linked with Tottenham this month and could be available on a cut-price deal from his financially struggling club, is a more advanced player than Fer so would not be a direct replacement.
Against West Brom it was Leighton Baines who provided the fire power with two first-half goals, before substitute Shane Long pulled one back after the break.
Afterwards, Moyes expressed his disappointment the Fer deal had not come to fruition.
"He is not our player but it is right we look after the boy and it didn't work for the reasons it didn't work," said the Scot.
"The boy is a very good player and we wish him well bit on this occasion we just couldn't quite conclude the deal.
"There are lots of things connected to signing a player: it could be a contract, it could be the agent, it could be the clubs and medicals as well.
"On this occasion some of them didn't come together.
"It is very late now so I don't know if we will be doing anything."
Negredo's agent Juanma Lopez has claimed that contact was made by Everton, but he says the deal was not feasible.
"It's impossible. Negredo is an important player for Sevilla and I am absolutely sure nothing will be done in this window," he told the Liverpool Echo.
"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."