Negredo has flown back to Seville to complete the transfer.
Manchester City are closing in on their second transfer from Sevilla this summer as Alvaro Negredo flies home from training to complete a £24.5m move, according to Marca.
The club will pay an initial fee of £22m, with a further £2.5m in add-ons.
Negredo would join Jesus Navas as players to join City from the Ramón Sánchez Pizjuán Stadium, with the winger having signed for the Citizens earlier in the transfer window.
The Sevilla squad are currently at a training camp in Costa Ballena, but the 27-year-old striker has flown back to Seville to finalise the move to Eastlands.
With the Spain international signing new City boss Manuel Pellegrini will be able to tick off one of the Chilean’s attacking targets, with Fiorentina’s Stevan Jovetic the other forward expected to make the switch to the Etihad Stadium.
The 2012 Premier League champions are desperate for new offensive talent after Carlos Tevez departed for Juventus and Mario Balotelli also left the club for AC Milan back in January.
This means that currently Sergio Aguero and Edin Dzeko are the only first team strikers at City, so new forwards are an absolute priority.
Negredo has been in fine form in La Liga for Sevilla since making a £13.2m move from Real Madrid in 2009, having scored 85 goals in 180 matches since the transfer.
The striker has also been capped 14 times for Spain, scoring six goals in that time.
The Spaniard would be the third new player to join City this summer, along with Navas and Brazilian midfielder Fernandinho, who signed from Shakhtar Donetsk.