The Sky Blues are believed to have been impressed by the Premier League’s top scorer this term – whose 25 goals have transformed the Reds from a team struggling to make Europa League qualification to one battling for the title.
Suarez was heavily linked with a move away from Anfield last year, but he has since penned a new contract to make him the Merseyside club’s highest ever earner with a wage in the region of £200,000-per-week.
Yet this has not deterred City, who are understood to have held tentative talks with the controversial star’s representatives.
But any deal would be difficult to strike, with Liverpool likely to demand a fee in the region of the world record one that took Gareth Bale to Real Madrid from Tottenham.
The 27-year-old has also spoken of his desire to play Champions League football with his current side, which looks to be likely to happen next season given their impressive form.
Suarez has put his spiky reputation behind him in recent times, and is widely being tipped for the PFA Player of the Year award.