The winger has been on the radar of Pep Guardiola for the past couple years as a Fernandinho replacement.
And now it appears that City are close to sealing a deal for the all action midfielder, per ESPN FC.
Another club that has an interest in Saul is Barcelona, as they want to reduce the age of their squad in key positions this summer.
But having signed Frenkie De Jong from Ajax, they already have an overload of midfielders at the club.
"He can't stay at Atletico anymore, everything's complicated for him there," a source told ESPN FC about Saul.