The league champions boss Roberto Mancini wants to offload controversy kid Mario Balotelli, who according to Manchester United left-back Patrice Evra, is homesick and wants to return to Italy.
Meanwhile, Suarez has kept Liverpool in the running this season, being the joint top-goalscorer with eight Premier League goals so far and with his current form Mancini wants to sign the Uruguayan to keep up with the title race against rivals Manchester United.
Liverpool have previously seen interests from cash-rich clubs Juventus and Paris Saint-Germain, both playing in the Champions League, and have successfully secured an extension to his contract which would keep him at Anfield until 2017.
However, manager Brendan Rodgers has insisted that Suarez will not be sold at any cost during the January transfer window but conceded that the club could lose their star man in case they fail to bring in reinforcements.
Liverpool have managed to keep some of their top players during the summer despite interests from top clubs across Europe. City tried to lure defender Daniel Agger while Anzhi Makhachkala wanted to sign Martin Skrtel.
The Reds have been linked to several strikers as they bid to add firepower to their depleted squad.