United trail Premier League leaders and city rivals Manchester City by 12 points following a 3-1 derby defeat at the Etihad prior to the international break, and are now seven points adrift of fourth-placed Tottenham.
But Mourinho believes eighth-placed United will have cut the gap to the Champions League positions by the end of 2018.
“It is a big gap but I know that until the end of December we have eight Premier League matches to play,” said Mourinho.
“If I’m not wrong I think there are eight.
“We are speaking about 24 points for us to fight for and the other teams that are in the top four. I believe we are going to be there.”