Ninety-six Liverpool fans died as a result of a crush at Hillsborough in an FA Cup semi-final between the Reds and Nottingham Forest in 1989.
United said the chants “have no place in the game”.
“It has always been the position of Manchester United that chants of this nature, which refer to historical tragedies, do not reflect the values the club holds,” a spokesman said.
“We are in discussion with our fans’ groups to seek their support in preventing this type of behaviour in the future.”
Former Liverpool midfielder Ray Houghton told BBC Radio 5 live the chants were “dreadful”.
“It has to come out of our game,” he said. “There were people in the crowd who lost loved ones at Hillsborough and that’s really hard to take.
“It’s something we don’t want to hear. It’s happened in the past with Liverpool fans to Manchester United with what happened at Munich. It’s uncalled for.”
In February 1958, eight United players and three club officials lost their lives in a plane crash in Munich following a European Cup tie.
“When you lower yourself to that level [of those fans], it’s quite remarkable,” said Houghton.
“It should have been a night of celebration – they haven’t played each other in a European tie before. The fans should have been getting behind their own team. When you stoop as low as they did last night, for me, it’s dreadful.”
A story in the Sun newspaper four days after the Hillsborough disaster criticised Liverpool fans’ behaviour at the time. The newspaper is still heavily boycotted in Merseyside as a result.
“It wasn’t continuous but it was clearly audible, maybe four or five times. It kind of got drowned out. The noise at the game was deafening.
“It happened again just after the full-time whistle – it was drowned out by: ‘You’ll Never Walk Alone’ and ‘we won it five times’ (a reference to Liverpool’s five European Cup triumphs). There was lots of saddened head-shaking in the press-box.”
Former United striker Dion Dublin told BBC Radio Manchester the songs were “disgusting”.
“It leaves a bad taste in your mouth,” he said. “It’s not in good taste, and the people that were actually singing it should feel embarrassed.”