The Mirror reports that Chelsea boss Andre Villas-Boas had a two-man delegation watch Pogba in action on Thursday.
Chelsea could make a bid of around £3million for the highly-rated midfielder.
Pogba has refused to sign a new deal with United and his current contract is set to expire at the end of the season.
Inter Milan are also reportedly interested in the young Frenchman.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.