They have reported the run of bets amid Spanish media reports that City have launched a £24m bid.
The Premier League runners-up were already considered favourites to secure the Spain international's services but have been cut from 11/8 to 1/2 due to the level of interest.
Negredo, 27, scored 25 goals for the Andalucian outfit as they endured a disappointing campaign, finishing ninth in La Liga.
Former team-mate Jesus Navas has already switched the Ramon Sanchez Pizjuan for the Etihad Stadium, joining fellow midfielder Fernandinho in signing for City this summer, while striker Carlos Tevez has left for Juventus.
Source: Manchester City MAD