Rashford has endured a stop-start opening to the campaign due to his sending-off against Burnley at the beginning of September, but the England international was free to face Young Boys in the Champions League.
However, the 20-year-old was substituted midway through the second half, and according to the Daily Mail, there was an exchange between Mourinho and his player after the game in Switzerland.
The report claims that Rashford failed to complete a full warm-down after the fixture, leading to Mourinho criticising the attitude of the academy graduate.
The Portuguese is currently involved in an ongoing dispute with midfielder Paul Pogba, while it has also been suggested that a number of players have grown frustrated with the conduct of their manager.
United currently sit eight points off the pace in the Premier League standings.