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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.