The People says after losing out to Real Madrid in the race to sign Spanish wonderkid Isco from his former club Malaga, Pellegrini is now eyeing up another swoop on La Liga. City raided Sevilla earlier this month to sign Jesus Navas for £15million.
And they are hoping to land Negredo, who has a £18m buy-out clause on a contract that still has four years to run.
The Spanish international is also attracting interest from Tottenham and Atletico Madrid, while West Ham have had a £14.5m bid rejected.
Negredo, who will be 28 in August, was the top home- grown goalscorer in Spain last season, with 25 of his 31 goals coming in La Liga.