The game ended 2-2 with Eric Choupo-Moting’s double cancelled out by Marcus Rashford and Romelu Lukaku.
Hughes could face FA action after pushing Mourinho out of the Stoke technical area as he was trying to give instructions to his defence.
The Times say the Potters boss could be in trouble if the officials include the incident in their post-match report.
Neil Swarbrick was in charge of the clash with Stuart Attwell acting as the fourth official.
All Premier League managers signed up to a technical area code of conduct back in 2015 aimed at stopping aggression from one to another on the touchline.
At the end of the match Mourinho shook the hand of every member of Stoke’s backroom staff but snubbed Hughes.
The Welshman was also angered by the Special one saying claiming that Saturday's game was ‘a match for [Marouane] Fellaini,’ implying that Stoke are a long-ball team.
“That's just an easy swipe at us, really,” Hughes said.
United return to action tomorrow night when they welcome FC Basel to Old Trafford in the Champions League.
Next up for Stoke is an away trip to Newcastle in the Premier League on Saturday.
