The Turkish ace has been on the radars of Premier League clubs for some time, after establishing himself as a key member of the La Liga high-flyers’ first-team.
City are believed to be plotting an end of season move, but their interest may kick Liverpool into life.
The Reds have already missed out on top target Mohamed Salah – who joined Chelsea – and may be reluctant to see another star they have been monitoring closely escape their grasp.
If the Merseysiders do make a concrete move, the Sky Blues may well enter the race this week.
Although City can offer him a more lucrative salary and guaranteed Champions League football, Turan may opt for Brendan Rodgers’ side after previously revealing that he would be open to joining the Anfield club.
The versatile midfielder only penned a new contract with Atletico earlier this season, but it is rumoured that that was a move to increase his release clause to ward off interest at the time.