The 19-year-old, who grew up as a Blues fan because of his father, completed a move from Southampton to Old Trafford during the summer transfer window.
Shaw faced his boyhood club last Sunday as United grabbed a late 1-1 draw on home turf, and while his father had previously cheered for Chelsea, he has now opted to switch allegiances.
According to London 24, when asked whether a draw was best for his dad, Shaw said: "No, no, no. My dad is a United fan now. He's not Chelsea no more. He is a United fan now and he won't be too happy because he wanted us to win really badly."
Ten points currently separate United from Chelsea, who are currently at the top of the league table.