Mourinho is targeting his 100th Barclays Premier League victory when the ailing champions - who were also the victims of his first win in that sequence in 2004 - visit Stamford Bridge on Sunday.
While Chelsea are in the midst of what appears to be a three-way title race involving Arsenal and Manchester City, United are 11 points adrift of the summit.
Floundering in seventh place, they may even fail to qualify for next season's Champions League with a five-point gap having opened up to fourth.
Moyes signed a six-year contract when he replaced Sir Alex Ferguson in the summer and Mourinho insists he will be given that time to build his own Old Trafford dynasty.
"I don't think there is a reason to have sympathy for David Moyes because he has a fantastic job," Mourinho said.
"He's very, very stable. The club gave him incredible trust when they chose him to be the next Manchester United manager after Sir Alex.
"It's a club with a fantastic culture. They believe in stability and the power of the manager. They believe in supporting the manager.
"Because they had a couple of bad results and they are not top of the league or as close to Manchester United as normal, (these) are not reasons for David to be in trouble.
"I think David is very stable and will have the time of his contract to build a team to achieve success and be there for many years.
"I don't think he's in trouble to have sympathy with, so no problems."
United travel to west London without injured strikers Wayne Rooney and Robin van Persie, but Mourinho still views them as a major threat that could yet win the Premier League.
"We don't play a team that is 11 points behind the leaders, we play the champions, we play against Manchester United," Mourinho said.
"This is the way I feel. I've been too long in the game. I've played dozens and dozens of derbies and classic matches. This is what experience says.
"On many occasions the team that looks to be in the most difficult situation is the team that appears stronger in that match. That's why I view this game as especially dangerous.
"I've not written United off. If you look at the table, obviously Arsenal and Manchester City are the top two teams.
"And Man City have different ammunition for such a difficult war compared to everybody else.
"But we are not far behind. Liverpool have a fantastic opportunity to do it because it's almost unique in that they're not playing in European competitions.
"And United are United. Eleven points from the leader is quite a lot, but they'll push all the way.
"The way this league is at this moment, for all the big teams, the first objective is to secure the top four. It'll be hard for everybody to do that."