The Portuguese coach was reportedly in the running to take over at Old Trafford last summer following the retirement of Sir Alex Ferguson.
However, United instead opted to follow the recommendation of the outgoing manager by appointing Moyes, who this week lost his job following a dismal 10 months in charge.
Mourinho, though, says he remains committed to his current club, who are still in the hunt for both the Premier League and UEFA Champions League crowns this season.
When asked if the Chelsea fans had cause for concern, he responded: "Of course not.
"I don't know how anyone could think about it. I left Real Madrid specifically to come to Chelsea and I signed a four-year contract.
"I told Chelsea they never have to worry about me because I don't want to leave. So I will stay here as long as the club want me to stay.
"There isn't any job that would move me from Chelsea."
Mourinho's side face Liverpool at Anfield on Sunday in a game that will go a long way to deciding who claims the Premier League title this season.
League-leaders Liverpool hold a five-point gap over the Blues with three games to go, with third-placed Manchester City six points off top spot with a game in hand.
Mourinho courted controversy this week by suggesting he would rest some players for the trip to Anfield in order to keep them fit for the second leg of their Champions League semi-final tie with Atletico Madrid the following Wednesday.
However, he refused to confirm or deny whether he would field an under-strength side at Anfield, saying that both his decision and the club's views on the matter were "private".
He added: "I want to win on Sunday. We will go to try and win. Nobody goes to a game to try and lose. If you wait until Sunday you will see my team."
Mourinho did confirm that captain John Terry and PFA player of the year nominee Eden Hazard would not be fit for Sunday's game and could also miss Wednesday's European tie at Stamford Bridge.
Mourinho was one of three Chelsea staff charged by the Football Association this week for their actions during the recent 2-1 loss to Sunderland.
The Blues boss was charged with misconduct for his post-match comments, in which he congratulated both referee Mike Dean for his performance and head of refereeing body Professional Game Match Officials Limited Mike Riley.
Chelsea made it clear that the charge would not be discussed at Friday's press conference, although Mourinho did add: "Every time I speak there is a consequence.
"Even if I say that a referee was amazing that was a reason to be with a charge. I can't say the truth. I don't feel free at all. If you want a better press conference, speak with the FA."
Asked about the British sense of humour and sarcasm, Mourinho added: "So Mr Bean is in jail...
"I told the referee he was amazing, and I repeat: the referee was amazing.
"I was not surprised (by the disciplinary action). In football I'm never surprised."
You can watch Chelsea's trip to Liverpool live on Sky Sports 1HD on Sunday from 2pm.