The classy striker has been one of the Sky Blues’ key men since his arrival back in 2011, and scored, arguably, the biggest goal in the Citizens’ history to clinch the title in 2012 – an injury time effort against QPR.
Aguero has hit close to 80 goals in total for his side, and his form has alerted Real.
The European Champions are believed to see him as a replacement for Karim Benzema, who himself has been impressive in the white shirt.
However, they would need to offload him before they can pursue a move for Aguero, and may also have to axe loanee Javier Hernandez to free up funds.
The City man has already spent some of his career in Madrid, playing for Los Merengues’ bitter rivals, Atletico.