The Brazilian, who joined the Red Devils in 2008, was linked with a switch away from Old Trafford during the summer.
However, a move never materialised and the 24-year-old has now turned his attention to seeing out the remainder of career with United.
"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," he told the club's official website.
Rafael made his first appearance of the season against Queens Park Rangers last weekend.