The Daily Mail said the issue had seen the club's food hygiene rating drop to two stars out of a possible five.
United are currently considering whether to redevelop Old Trafford or build a brand-new stadium.
"Manchester United implements a robust pest-control system throughout Old Trafford," a club spokesperson told the Mail
"Multiple weekly checks are made in all catering areas and stringent measures are taken to ensure levels of hygiene and cleanliness are high wherever food is stored, prepared and served.
"If incidences of this nature do occur at the stadium, immediate and appropriate action is taken."
A Trafford Council spokesperson said: "Our environmental health officers gave a food hygiene rating of two following a routine visit.
"We are now working closely with Manchester United to ensure it complies with the rating and carries out the necessary improvements."
United, who sacked manager Erik ten Hag earlier this season, suffered a 3-0 defeat at home to Bournemouth on Sunday - a reverse that left the former Premier League kings a lowly 13th in the table.
During new boss Ruben Amorim's post-match press conference, a leak from the ceiling of the media conference room at Old Trafford resulted in water dripping onto the front row of journalists.
