The former Real Madrid ace is now in his third season with United.
"Since the first minute, I have felt at home," he told the United Review.
"Since the first day, stepping into Manchester Airport, I felt at home, I felt so good. So I just want to thank everyone for the love and support, and I want to repay this on the pitch.
"Everyone wants to win, but my thoughts when I step onto the field of play is to do my best, not just for me or my family, not just for the club, but for the fans. You always have to think of this.
"From day one, the love and support from the fans has been unique and special, it surprised me a lot. I value and enjoy every moment, as I feel so much affection for them."
Casemiro has made 101 appearances for United since his 2022 arrival.
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