Negredo, who scored 25 Primera Division goals last season, is set to link up with his former team-mate Jesus Navas, who moved to City from Andalucia earlier this summer.
Del Nido told the Spanish club's website: "We are about to close on the sale of the player and, if everything goes normally and everything is signed, he will soon say goodbye to the Ramon Sanchez Pizjuan.
"Manchester City are buying a great player, the top-scoring Spaniard in La Liga.
"This is a big deal for Sevilla, the second most important in our history after we sold Daniel Alves to Barcelona, and the player will sign the contract of his life.
"Everyone should be happy; it is a great deal for all three parties."