Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
Negredo has been linked with a move away from the Andalusian outfit for the last few months and it now seems increasingly likely that the Spain international will be plying his trade elsewhere next season.
According to Del Nido, Negredo wants to play Champions League football, something Sevilla cannot offer him next season after only finishing ninth in the Primera Division in the recently-completed campaign.
Del Nido has also revealed that Sevilla have had two offers for the 27-year-old, one from Atletico Madrid and the other from a foreign team.
"An operation of this type has three parties: Sevilla, the club who want to buy and the player," Del Nido told Sevilla's television channel.
"One of the parties, which is the player, wants to go. Because of that we are already a little forced in our negotiations. We need to weigh up if it's good for a player to stay against his will.
"The player hasn't put his foot down and told me 'I want to go', but he has said that he wants to develop and wants to play in the Champions League.
"We won't forget that that will of the player is very important for making a decision."
When asked how much it might take to prise Negredo away, Del Nido said. "If we start talking about fees...the players are valued according to the transfer market and who knows that better than us.
"What is a player who scores 30 goals a season worth? Negredo went to the European Championships, (Valencia striker Roberto) Soldado went to the Confederations Cup, Soldado-Negredo, if you see what Soldado is worth on the market, you'll see what Negredo's worth.
"I've spent 30 years buying (players) and I know what he's worth. We are calm with Negredo, we've already rejected a first offer."
The Sevilla chief added: "Currently there are two offers, one from Atletico and another from a foreign team which we are not going to say who."