The Uruguayan has been in fine for the for the Reds so far this season, netting 11 goals in all competitions.
These performances have not gone unnoticed and the City coach now sees the Uruguay international as the ideal candidate to strengthen his attacking options.
Any move would likely spell the end for Mario Balotelli, who is believed to have frustrated the Italian manager in recent weeks.
Prising the forward away from his club would be difficult and command a huge fee, suspected to be near the £50m mark.
Suarez penned a new deal with the Merseysiders during the summer which runs until 2017 and puts him on a par with the likes of Steven Gerrard in terms of weekly wage.
This, coupled with the team’s support of him through the racial abuse allegations last season, has strengthened Suarez’s relationship with the club meaning he is unlikely to attempt to force the move.
Liverpool are also unwilling to sell their star, as was shown in their rejection of moves from Juventus and Paris Saint-Germain during the last transfer window.
However, the 25-year-old may be tempted at the end of the current campaign if the Anfield outfit fail to show suitable signs of progression.
A move to the Etihad Stadium would guarantee a challenge for top honours, which could be enough to turn the controversial attackers head.