The Merseyside club have identified the Swedish striker as a potential bargain buy, after he spent almost 18 months out of the game through illness.
Guidetti, 21, last played competitive football on loan at Feyenoord where he scored 20 times in 23 matches, but is now struggling to get a chance at the Etihad Stadium with their four main strikers blocking his path to the starting line-up.
Monaco and Trabzonspor, who attempted to sign the Swedish hitman in the summer, are also in the race for his signature but he is understood to prefer a switch within England.
Liverpool are committed to bringing through young talent and with Guidetti able to play up front or on the wing, he offers real versatility for Brendan Rodgers.
City would want at least £5million for the youngster, who still has 18 months left on his contract.