The Manchester United Supporters Trust has invited Jose Mourinho to a meeting to discuss "concerns" that the manager may have.
The Portuguese coach has created a tension between himself and the fans following Saturday's 1-0 victory over Tottenham Hotspur at Old Trafford.
The 54-year-old appeared to tell doubters to calm down by raising his finger to his mouth, and later criticised them for their treatment of Romelu Lukaku, who has not scored in his last six outings.
Ahead of Tuesday night's 2-0 victory over Benfica in the Champions League, Mourinho took another subtle swipe at the fans in his programme notes by saying that he hopes that they enjoy the game more than some did against Spurs.
In response to the manager's recent behaviour, MUST released a statement, which 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.
"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."
United currently sit second in the Premier League table, five points adrift of leaders Manchester City.
