The Dutchman, voted United's player of the month for December after scoring five goals in their six league games during that period, thanked the fans for their support.
Speaking to the club's official website, Van Persie said: "It's always nice to be recognised by the fans.
"I have settled into the club quite quickly and I am really enjoying playing in this team. I would like to thank the fans for all their support.
"It's not all about scoring goals, but obviously that does help. It's great that so many players have scored goals over the season so far.
"December is always a difficult month and I feel we have come through this period as we wanted to and hopefully we can now push on for the rest of the season."