While Jose Maria del Nido insists neither Manchester City nor Tottenham have bid for Negredo, it has been reported that the Sevilla president held talks with the City chief executive Ferran Soriano on Wednesday.
But amid suggestions of further interest from Tottenham, Del Nido stressed on Thursday that he would not negotiate a cut-price deal with any club and declared that, for now, the forward remains a Sevilla player.
He said: "Sevilla have an asking price for Negredo and if it isn't met, he will play for Sevilla next season. Tomorrow he will sleep in Seville and then he will start training with the team again.
"There have been no offers from English football, not from City, not from Tottenham."
Speaking to reporters at a promotional event, Del Nido also declared that the Argentine centre-back Nico Pareja would join the club on loan from Spartak Moscow next season, with Sevilla retaining the option to buy him when the loan deal expires.
"I've spoken to him and we still need to iron out some details with Spartak, but if there are no complications, Nico Pareja will travel to Seville tomorrow (Friday)," he said.
"The player has made a huge effort to come to Sevilla by renouncing part of his contract, and I am as excited about signing him as I am about any of the big names in football."