A club official told Reuters they would be making no response to the story in Spanish newspaper El Pais which cited sources close to former Chelsea manager Mourinho.
The Portuguese, who also managed Real Madrid and Inter Milan, has been persistently linked in the media with the Old Trafford job since departing Stamford Bridge for the second time in December.
United, who are sixth in the Premier League, face fourth-placed Manchester City later on Sunday needing a result to boost their chances of qualifying for the Champions League.
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Under the terms of the agreement, the El Pais report said, United would have to pay Mourinho five million pounds ($7.24 million) if they did not offer him a full contract by May 1 and another 10 million pounds if they failed to give him the job by June 1.
Van Gaal signed a three-year contract in May 2014 but is not expected to see out the deal with fans unhappy with the style of play and poor results.
The report, which cited a source with links to the company run by Mourinho's agent Jorge Mendes, said United wanted a flexible deal because of a split in the Old Trafford board as to whether the 53-year-old was the right choice for the club.
(Additional reporting by Nick Mulvenney; Editing by John O'Brien/Toby Davis)
