Representatives from the Premier League pair were believed to have been in attendance for the Scottish side’s 4-1 win over Partick Thistle, and were impressed by the 17-year-old, who played a part in all of the goals.
Gauld has been earning rave reviews for his performances north or the border, with some even comparing him to Barcelona superstar and Ballon d’Or holder, Lionel Messi.
Real Madrid have been linked with a stunning swoop for the teenager’s signature, but now Liverpool and United are thought to be leading the race.
Scouts from both clubs are believed to have been impressed by the youngster, which could prompt January offers.
Dundee United are thought to be desperate to keep Gauld, but may be willing to do business for around £6m.
Despite being 17, the midfield man already represents Scotland at U-21 level and is expected to graduate to the senior set-up in the not too distant future.
Both Liverpool and United have had a number of Scottish players throughout their histories, and are said to be ahead of the likes of Everton and Newcastle, who are also watching the wonderkid.
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