The Brazilian has been part of the first-team set-up since 2008, and made his first competitive start under Louis van Gaal in last weekend's 4-0 thrashing of QPR.
Rafael has seen fellow defenders Rio Ferdinand, Nemanja Vidic and Patrice Evra all depart the club in the off-season, but the 24-year-old has his sights set on a long stay in Manchester.
"I am glad but sad because a lot of friends have left," he told the club's official website. "I am glad I am still here.
"I want to keep going and stay here forever, if possible. It depends on me to play well, I need to play well. I just want to stay here.
"When I first came here, I saw how a lot of players helped me - [Ryan] Giggsy, [Paul] Scholesy and Gary Neville, even though he played in my position, he helped me a lot because he was one of the best right-backs in the world.
"I want to do the same when I see some young players come in. Sometimes it's difficult so my job is to try to help them.
"I have a good relationship with the fans because they are just so passionate.
"The fans here at Manchester United are simply so good at every game, even if we lose, they are still singing and just don’t stop singing and making noise! It makes you get emotional. I love these fans."
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