The 23-year-old is a top young prospect, and looks set to have earned himself a move to a bigger club in this transfer window after his hugely impressive form in Portugal in recent times.
According to a report from the Daily Telegraph last month, it looked like Arsenal could be close to winning the race for his signature, but this move never materialised, with Arsene Wenger’s side still to add a quality addition in the middle of the park this year, despite it being something of a problem position for the team last season.
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Carvalho could have been a good addition for the Gunners, but he could also be in with a chance of commanding a place in the Real Madrid starting lineup next season, with Rafael Benitez’s side perhaps in need of a more defensive-minded option over players like Toni Kroos and Luka Modric.
Sami Khedira has also left the Bernabeu for Juventus this summer, while rumours elsewhere suggest that Liverpool could be looking to sign Asier Illarramendi from the Spanish giants, according to the Metro.
Carvalho would join fellow countrymen Cristiano Ronaldo, Fabio Coentrao and Pepe if he does move to the Spanish capital.