United enjoyed a stellar start to the season as their bright, enterprising football helped them to keep pace with Manchester City.
But they've since stumbled and Mourinho has been accused of reverting to the defensive tactics that have otherwise served him well during his career.
Some United fans have voiced their disapproval towards that approach and Mourinho was booed on Saturday when he subbed Marcus Rashford off against Tottenham.
Rashford's replacement, Anthony Martial, bagged the winner against Spurs and Mourinho gestured towards the camera at full-time - a shushing action read by some as a message to fans.
MUST would certainly appreciate the opportunity to engage with the manager
Manchester United Supporters Trust (MUST) statement
The Portuguese also aimed a dig in his programme notes for the Benfica game on Tuesday night, saying: "I hope that you enjoy the game more than some of you did against Tottenham."
Manchester United Supporters Trust (MUST) have now invited Mourinho to speak to them in the wake of the tension.
A MUST statement read: "There are differing views amongst supporters on precisely how to interpret the manager's comments.
"However it's probably fair to say there is a universal desire within the stadium to see atmosphere improved just as there is at other Premier League clubs.
GETTY
Jose Mourinho appeared to take issue with Manchester United fans after the 1-0 win over Tottenham
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Allardyce puzzled by Man Utd fans' anger at Mourinho's tactics
GETTY
A section of Manchester United fans booed Marcus Rashford's withdrawal against Tottenham on Saturday
"There are a number of factors that have contributed to atmosphere decline over the decades, some of which could be addressed with better co-operation between clubs and supporters.
"MUST would certainly appreciate the opportunity to engage with the manager, as part of our existing dialogue with other club officials, on issues around atmosphere and would be more than happy to meet to discuss his concerns."
Second-place United are back in Premier League action this weekend.
Mourinho's men visit Stamford Bridge to take on Chelsea on Sunday (4.30pm).
