The Red Devils are 13 points adrift of top spot in the league in ninth place, having struggled to adapt to life under new boss David Moyes.
But the Portuguese believes the Old Trafford side have what it takes to challenge for honours.
"They have to recover points not to one single team, they have to recover points to every other team," Mourinho said. "It's difficult. Not just because it's 13 to Arsenal, but also because it's eight to us and to Liverpool and seven to City.
"But as I keep repeating, the culture of Man United is there, the power and the quality of their players is there, the tradition is there.
"When mathematically it's very possible, I never say Man United is out of the race."
Mourinho is well aware the results over the festive fixture programme can have a major say on the destination of the trophy come May.
"Let's see if after Christmas we can say instead of six (contenders), five," Mourinho said.
"Maybe one drops back or maybe one goes so up that it looks impossible to reach.
"It's very difficult to predict the way things are going. One thing is if we beat Arsenal, another thing is if Arsenal beat us. We can close the gap or they can open the gap.
"This weekend Tottenham-Liverpool, somebody loses points, us against Arsenal, somebody loses points, Arsenal against City, somebody loses points."
Chelsea's aim is to stay in contact.
Mourinho added: "Five points is a gap that is not a drama, but we have to try (to ensure) that the five-point gap doesn't open, at least.
"With a five-point gap (and) two matches (in) one week, everything can change.
"When you go instead of five to eight, nine, 10 (points), the situation is more complicated."
Mourinho, who won the title in 2005 and 2006 in his first two seasons with Chelsea, has long insisted the challenge on his return is more difficult, with a squad in transition.
He wants his players to have the mentality of one of the favourites, even if he believes other sides have a better title chance, after finding a team built for the short-term under his predecessor Rafael Benitez.
Mourinho added: "Benitez was chasing results. He was not worried about the building up of a team with a certain style. We didn't have a real base to start with.
"For many reasons we knew that the situation needs time and patience. We are competing against important teams in a very difficult league where you don't have one single easy match. We knew it would be difficult.
"We are not favourites, but we want to feel as favourites. We want to fight the favourites and we want to feel like we are.
"To put ourselves under a little bit of pressure only can help to be better. I want that."
Whether Mourinho is afforded the patience others have not at Chelsea remains to be seen, but what is in little doubt is that his side are favourites for Saturday's London derby with relegation-threatened Palace.
Defender Gary Cahill will be rested, with the upcoming fixtures in mind.
Mourinho said: "Is he injured? No. He is almost injured, so we decided to kill the almost and to protect the little pain he is feeling on his quadriceps."
Ashley Cole will return to the substitutes' bench, with Spain right-back Cesar Azpilicueta taking his place at left-back, and is instead selected for next week's Capital One Cup quarter-final at Sunderland.
Mourinho, who would not comment on reports Chelsea are targeting Southampton's Luke Shaw as a long-term left-back successor to Cole, added: "In positions I can, I need fresh people. I need Azpilicueta to play tomorrow, I need Ashley Cole to be fresh to play in Sunderland.
"I trust both. I choose the one I think is better for the occasion. It's good to have options."
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