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Semenyo has two goals in four appearances in the competition, and another two goals and two assists in League Two.
Bristol City's loan manager Brian Tinnion confirmed United had sent scouts to watch Semenyo play.
He told 'Robins On The Wire' podcast: 'I was sat with a Man United scout at Newport the other week, to be honest, and they really like him.
The Sun claim United are considering making a move for Semenyo to snap him up before other clubs get wind of his talents.
Semenyo made his senior debut for Bristol City in May, coming off the bench to play eleven minutes against Sheffield United in the Championship.
Newport have offered Semenyo the chance to play up front, but have also used him on the left and ring wing.
MORE: Romelu Lukaku considering transfer away from Manchester United.