The Manchester-based official was appointed for the high-profile Premier League clash despite his potential close association with the Red Devils, which left Liverpool fans unhappy on social media.
Keith Hackett, the ex-head of the Professional Game Match Officials Ltd, was among those to criticise the decision to put Taylor in charge of the fixture, saying that "it would be intolerable" if there were a disputed call in the derby.
Mourinho believes that it could be a tough evening for the 37-year-old, telling reporters: "I think Mr Taylor is a very good referee, but I think somebody with intention is putting such a pressure on him that I feel it will be difficult for him to have a very good performance.
"Our own disciplinary record is really, really good. We don't have problems at all at this level. We are a team that plays with discipline, that is following everything that was told to us in the meetings that we had with the representatives of the Premier League and the referees.
"We don't press referees, we behave on the touchline so that's a point that we are very comfortable with."
Mourinho also called on supporters of United and Liverpool to be on their best behaviour after both clubs were fined for derogatory chants in last season's Europa League tie.