The Red Devils regained a place in Europe’s top competition after finishing third in last season’s Premier League.
After been allocated in Pot Two, Ole Gunnar Solskjaer’s side were drawn in Group H with Paris Saint-Germain, RB Leipzig and Istanbul Basaksehir.
On paper, Group H looks one of the toughest but Hargreaves believes Manchester United should be ‘quietly confident’ about progressing to the knockout stages.
However, the former United, Bayern Munich and England midfielder says the club should be looking to bolster Solskjaer’s squad with a couple of signings before the summer transfer window closes on October 5.
Reacting to Manchester United’s Champions League draw, Hargreaves said on BT Sport: ‘I think they can be quietly confident.
‘PSG are the strongest team in the group but I think United are the second strongest team.
‘RB Leipzig have a brilliant young manager who will relish playing against United.
‘We know that they’re not firing on all cylinders but hopefully they get a few players in. It’s a big season for United and Ole Gunnar Solskjaer.
‘[The draw] is not ideal but hopefully they can get a few players in and finish first or second.’
Former Liverpool and England star Steve McManaman added: ‘It will be difficult for United if they don’t bring any new players in.
‘They’ve obviously been to PSG before and won, when Solskjaer effectively secured his job. Leipzig are in good form and that is another tough game.’
Ex-Tottenham and England boss Glenn Hoddle, meanwhile, has given Manchester United hope of reaching the knockout stages despite landing in the ‘toughest group’.
‘They have got the toughest group, for sure. They have some tasty games,’ he said.
‘They’ve been trying to get players in. It’s difficult when you can’t get your top option because then you have to work quickly.
‘They’ve got to get back to how they were playing at the end of last season. There’s not massive pressure on them.
‘They’re a work in progress. I don’t think they can win [the competition] but the pressure will be off them.’