The Daily Star says United scouts have also kept close tabs on Huddlestone's progress at White Hart Lane in recent months.
The 23-year-old has arguably been the Premier League's most improved central midfielder over the past 12 months and his passing ability and range has impressed Sir Alex Ferguson.
Spurs boss Harry Redknapp will fight tooth and nail to keep hold of his star midfielder, who has played an integral role in the north Londoners' recent resurgence.
The former Derby County powerhouse would cost £20m given his status as an England international and his young age.
But Fergie would be willing to offer Redknapp former Tottenham star Michael Carrick as a makeweight in the deal.