Aguero has endured a mixed season at Manchester City under Pep Guardiola.
The Argentina international has flitted in and out of the side despite scoring 13 Premier League goals from 17 games.
He briefly lost his place in the City XI to Gabriel Jesus before the Brazilian's injury last month.
Sergio Aguero could leave Manchester City for Real Madrid
Five most likely summer deals according to the bookies
Wed, February 1, 2017
Express Sport takes a look at the five most likely deals that could happen this summer. Odds provided by BetStars
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Griezmann to the Premier League – Man Utd 15/8, Chelsea 6/1, Man City 8/1
Sergio Aguero has endured a mixed season at Manchester City
His failure to convince Guardiola fully of his ability has led to talk he could join fierce rivals Chelsea.
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But France Football claim Aguero could be off to Real Madrid instead.
It is claimed president Florentino Perez met with City chairman Khaldoon al-Mubarak last week.
They shared dinner together and Aguero's name was reportedly raised.
Isco has made just 13 appearances for Real Madrid
Perez then proposed to al-Mubarak a swap deal with Isco heading in the opposite direction.
The Spain international has struggled for game time at Madrid making just 13 La Liga appearances.
With Barcelona circling, Perez could use him to ensure he lands Aguero, who could replace the toiling Karim Benzema.