The Spanish giants have been linked with the Argentine for some time, and are now ready to sell Karim Benzema to fund a move for his signature.
Real are willing to take £35m for their current main forward – with Paris Saint-Germain keen – which they will then use as part of a deal to lure Aguero back to La Liga.
The 25-year-old previously played for Los Blancos’ city rivals Atletico Madrid, where he developed a reputation as one of Europe’s top strikers.
City are unlikely to be open to doing business, but Real’s president Florentino Perez is expected to get personally involved in the situation to persuade the player himself to agitate for a transfer.
Aguero cost the Sky Blues £38m in 2011, and starred in their Premier League title win in his debut campaign.
He is still thought of as one of the club’s key men, with his absence through injury having contributed to their slide away from league leaders Liverpool in recent weeks.
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