United host PSG tonight in the first leg of their last 16 tie with the French champions.
When the Red Devils were pitted against the Parisians eight weeks ago they were not given a chance.
But Jose Mourinho was sacked the day after that draw and since then the club has been revitalised by the arrival of Ole Gunnar Solskjaer.
The Norwegian coach temporarily left his post at Molde in order to assume caretaker responsibilities of the team, and has led them to 10 wins out of 11 since.
Solskjaer famously scored the winning goal in United’s 1999 Champions League triumph over Bayern Munich, and now has the chance to clinch glory as a manager.
That still seems far-fetched, with United the underdogs to progress into the quarter-finals, let alone win the competition.
But former United midfielder Fletcher, who won the Champions League in 2008 at United, believes the club can do exactly that – starting with a positive start tonight.
Asked on talkSPORT whether United could win the Champions League, the Scotsman said: “Yeah, without a doubt.
“The Real Madrids and Barcelonas of, old who everyone fancied to win it, they’re are not quite where they used to be.
“It’s very open, and Man United are hitting form at the right time.
“And I think worse teams than this Man United team have won the Champions League in previous history, or at least get to the latter stages of the finals.
“I have seen worse teams go all the way. Sometimes in this tournament it’s not necessary the best team that wins it, it’s the in-form team.
“They’ve definitely got the capabilities, they’ve got the match winners, and Ole definitely has got that Manchester United mindset. He’ll be thinking: ‘We can win this competition.’
“The Old Trafford crowd will be absolutely rocking tonight and I think it could take them a long way.”