The England international forward has been linked with the Blancos for some time, but he is currently tied to a long-term contract at the Etihad
He has, however, seen his fine form under the guidance of Pep Guardiola attract plenty of admiration from afar.
End product has been added to the 25-year-old’s game, with the 2019-20 campaign seeing him break the 20-goal barrier in a third successive season.
La Liga giants Real would welcome the opportunity to buy into that productivity and add another ‘Galactico’ to their ranks.
Sterling is aware of the rumours, but claims there is no substance to them at the moment.
He told AS as City count down the days to the first leg of a heavyweight Champions League last-16 showdown with Madrid: “It’s one of those things… Right now I’m at City and I’m really happy.
“But Real Madrid are a fantastic club, when you see the white shirt you know exactly what the club stands for, it’s massive.
“But at the same time, I have a contract with City now and I have to respect this. But it’s a fantastic club.”
Sterling added when pressed further on the interest he is generating in Spain: “It’s something that you see all the time, but I’m a City player and I’m enjoying it at the moment, even if things haven’t gone quite to plan in the league.
“We now have a massive opportunity in the Champions League but I keep saying, Real Madrid is a fantastic club, there’s lovely weather but I am quite happy at City.”
Sterling has admitted in the past of harbouring the ambition of one day leaving England for warmer climes.
Madrid could be considered the perfect destination.
He concedes that anything is possible, with a chance that he could one day line up for the Blancos.
Pressed on whether he would welcome that opportunity, Sterling said: “How do I answer that one? Is the camera live or is it just taking pictures?
“No one knows what the future will hold. I am a player and I am always open to challenges but right now my challenge is at Manchester City. In the future, hopefully, who knows…”
Sterling is currently trying to rediscover his spark at City, with eight games passed since he last found the target for a club that remains in the hunt for Carabao Cup, FA Cup and Champions League honours.