The Independent on Sunday also claims Mourinho offered a "forensic analysis" of the Old Trafford squad in what it called a "love letter" to the club.
United were booed off after Saturday's 1-0 home loss to Southampton.
Mourinho, 52, is available after being sacked by Chelsea in December.
Mendes said the idea of the Portuguese writing such a letter was "ridiculous", adding in a brief statement: "It does not occur to anyone that a coach like Jose Mourinho can write letters to clubs offering their services."
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After the Premier League defeat by the Saints, during which United managed only one shot on target, Van Gaal said he and his team deserved to be jeered by their fans.
"They are right to boo. I cannot deny that, I saw the match," said the 64-year-old Dutchman.
United, who are fifth in the league and five points off the Champions League places, have taken 37 points from their first 23 games - their lowest total in the Premier League era.
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A report claiming Jose Mourinho wrote a six-page letter to Manchester United outlining his suitability to succeed Louis van Gaal as manager is "totally absurd", says his agent Jorge Mendes.