The 24-year-old is believed to have become increasingly disillusioned with life in England following the break-up of his marriage - to Diego Maradona's daughter, Giannina - and is ready to return to Spain this summer.
Aguero's estranged wife has moved back to Madrid with his son, and the South American star is finding it increasingly difficult to be away from his family.
A Spanish source told Starsport: "Sergio's personal life has become complicated, but a move to Real Madrid would certainly help his situation."
Citizens boss Roberto Mancini will be desperate to keep hold of his leading striker, particularly while question marks continue to surround the long-term future of Aguero's compatriot, Carlos Tevez.
Real Madrid tried to sign the Manchester City hit-man 18 months ago when he left local rivals Atletico Madrid, but Los Rojiblancos chiefs refused to sell their prize asset to their neighbours.
However, Aguero has always remained on the radar of Santiago Bernabeu president Florentino Perez, and now Real Madrid are ready to offer Manchester City £45million to bring him to the capital club when the transfer window reopens this summer.
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