The Sunday People reports that United are on the verge of a bid for the 17-year-old, who has been compared to Lionel Messi.
The youngster has been hailed as one of the hottest teenagers in Europe and has also been linked with Spanish giants Real Madrid.
United boss David Moyes reportedly sent his aide Jimmy Lumsden to watch Gauld make his Scotland Under-21 debut against Georgia last week.
Reports claim Dundee United are prepared to sell Gauld for around £5million.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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