It is understood that a figure of £22m has been agreed between the two clubs, with the 27-year-old due to complete his move to the Premier League outfit in the next 24 hours.
"We are about to complete the sale of Negredo to City. If all goes well he will say bye this afternoon at the Sanchez Pizjuan," he told reporters at a press conference.
"City are signing a great player. For Sevilla and Negredo it is a major operation. It is the contract of his life."
Negredo scored 31 goals in 42 games for Sevilla last season.