The Sun says neighbours have complained about the 18-year-old's two French bulldogs and the noise they make.
Rashford bought the duo after signing a new £20,000-a-week contract at Old Trafford following a successful breakthrough season.
United are now paying for two experts to train the dogs at the striker's home in Altrincham, as he spends a considerable amount of time away for training and matches with the club.
A source said: "It makes a change from the usual calls we get from players' girlfriends.
"Marcus is a young player and he can't be in the house all the time because he is training.
"That's why the club had to find a specialist to get them house-trained."