Barcelona have been backed to sign Silva this summer after the 22-year-old inspired Monaco to the Ligue 1 title.
Manchester United are also keen, with Jose Mourinho coy on a bid for the midfielder following the club's Europa League final win over Ajax last night.
However, despite winning the Spanish title and being on the brink of a third Champions League win in four seasons, Cristiano Ronaldo wants Real to bolster their ranks for next season.
United goalkeeper David De Gea is on their radar, two years after the Spain international was the subject of a failed bid from Real on transfer deadline day.
Real Madrid's top summer transfer targets Tue, April 25, 2017
Express Sport runs through Real Madrid's top summer transfer targets
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Who will Real Madrid sign in the summer transfer window?
Cristiano Ronaldo wants to scupper Barcelona and Manchester United's transfer plans
Cristiano Ronaldo has personally requested Real Madrid sign Monaco star Bernardo Silva
And they are also in for Monaco and Chelsea stars Kylian Mbappe and Eden Hazard.
But Spanish outlet Don Balon say Ronaldo has personally requested the signing of Silva – and is hoping his agent Jorge Mendes can broker a deal.
Mendes manages both players' affairs and his influence could prove key to beating Barcelona and United to the Portugal international's signature.
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Bernardo Silva fired Monaco to the Ligue 1 title this season
Ronaldo feels that, with Silva in the team, his chances of continuing to score goals would be improved.
With Karim Benzema's future up in the air, Real could tinker with their formation next season and Ronaldo supposedly feels his compatriot would be a fine acquisition.
And with the club set to earn more success, with Ronaldo at the forefront, they could grant him his wish.