According to 'Sky Sports', Real Madrid are eyeing a move for the England international, but with Friday's European deadline looming, it is unlikely an offer with be made.
'Los Blancos' are tracking the player's progress and will have representatives of the club watching on as England take on Spain in the UEFA Nations League in September.
Sterling, 23, has less than two years left on his current Manchester City deal, and talks over a new contract seem to have stalled in recent months, despite Kevin de Bruyne, David Silva, Fernandinho, Gabriel Jesus and Nicolas Otamendi all having pledged their future to City this year.
The winger scored 23 goals in 46 appearances last season, and already opened his account for this campaign with an impressive goal against Arsenal on the opening day.
However, Sterling faces competition for his place in Pep Guardiola's side from new signing Riyadh Mahrez, adding to the already formidable duo of Bernardo Silva and Leroy Sané.