Mourinho's position at the club has been under scrutiny this season, with the Red Devils eighth in the Premier League, eight points off the top four.
The Portuguese, 55, signed a contract extension at Old Trafford in January but has been linked with a return to former club Real Madrid.
"It's totally untrue," said agent Jorge Mendes in a statement.
"Jose is very happy at the club and the club is very happy with him. He has a long-term contract with Manchester United and is fully committed to the club in building a solid winning project."
While Mourinho has been linked with Real, there have also been media reports suggesting United are considering bringing in Tottenham manager Mauricio Pochettino to succeed him.
United play Fulham at home on Saturday before trips to Valencia in the Champions League on Wednesday, and Liverpool in the league on 16 December.
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