The online bookmaker 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 swapped 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.
Sky Bet Football Trader Chris Spicer said: "Atletico Madrid had been backed to land Negredo following Falcao's departure but the last few days have seen City emerge as favourites.
"Additional firepower looks essential given their troubles in front of goal last season and they have previously been backed to bring in Isco and Edinson Cavani, but Negredo now looks to be their number one target."