David Moyes' men have struggled to keep pace with their title rivals and they slipped 12 points behind leaders Arsenal after the midweek 1-0 defeat by Everton.
But Mourinho, who was once touted as a possible successor to Sir Alex Ferguson, believes the winners' mentality at United will ensure they stay in the hunt.
The Portuguese coach is certain that United's board and playing staff will remain calm and predicts more twists and turns in the title race.
"If it was another club I'd tell you it's impossible, but with Manchester United I don't say that," said Mourinho.
"The reasons are because of the potential of the team, what the club represents and the culture of the club.
"It's not a club in panic. It's not a club where you feel the end of the world is arriving.
"They are calm, they go the same way and support the manager. Nobody touches the manager.
"They have a project. If they don't win this season they believe they will win next season.
"It's a very, very stable situation and an example to many others. Because of that they are still a contender.
"They will stick together, they will fight and try to get 12 to 15 points in a row. Yes they are still a contender.
"They will wait for matches between Chelsea, Arsenal, Manchester City, Liverpool and Tottenham when others will lose points."
Mourinho admits Arsenal are worthy front-runners, but knows there is still plenty of time to close the four-point gap at the top.
"Arsenal lead and if they lead it's because they have more points than other people and because they are better and have made less mistakes," he said.
"If they are there it's because they deserve to be there. But the championship finishes in May. Let's see what happens then."
Chelsea travel to Stoke on Saturday to conclude a run of three Premier League matches in seven days, while Arsenal have faced the same number of games over nine days.
Mourinho is fully aware of the discrepancy, describing it as a 'big coincidence'.
"This is like preparation for the Christmas period," he said. "This week is a hard week because we start on a Sunday, not even on a Saturday, playing Southampton, but finish on a Saturday.
"For some clubs it's Saturday-Sunday when for us it's Sunday-Saturday.
"Once more when it comes to fixtures, we are always in trouble. It's a big coincidence.
"I don't like to give a day off to the players after a big game, but I'll have to give them the day off on Sunday.
"I don't think it's good for their body, but it's good for their heads.
"I like to give physiological recovery, but the mental point of view is more important. It's important they have a free Sunday to disconnect."