The Brazil international joined the club from Fluminense alongside twin brother Fabio in 2008, but has yet to secure a regular first-team berth.
However, his manager insists that at just 21 years old, Rafael can go on to become one of the best in his position given his development since joining the club.
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"The boy has developed immensely since joining United, his energy and enthusiasm are a joy to watch.
“Rafael is one of the club’s brightest young prospects; he has no fear of playing and has great belief in himself."
The right-back thanked his manager for his support and spoke of his desire to continue bringing trophies to Old Trafford.
Rafael said: "I love playing for Manchester United, there is a great team spirit here and a real desire to win.
"I would like to thank Sir Alex for his belief in me and I would also like to thank the fans for their support.
"My time here has been unbelievable; winning two league titles, a league cup and a Club World Cup has made me hungry for more trophies."