United fought back to beat Greek champions Olympiakos Piraeus 3-0 on Wednesday and book a place in the last eight of Europe's elite club competition 3-2 on aggregate ahead of Friday's quarter-final draw.
The achievement helped mask their struggles in the Premier League, where they sit seventh, 18 points behind leaders Chelsea, with nine games left of their title defence in Moyes's first season in charge.
"For some reason, the team's best performances have come in the Champions League," Scholes told reporters in Singapore on Friday after hosting a training session for local youth players.
"If they play like they did on Wednesday, I don't see why they can't reach the final.
"It's been a difficult season so far, but getting to the final of the Champions League would make for a good ending."
United go into the quarter-final draw along with Spanish trio Barcelona, Real Madrid and Atletico Madrid, domestic rivals Chelsea, big spending Paris St Germain as well as German duo Borussia Dortmund and Bayern Munich.
Moyes has overseen five home league losses this term, including shock defeats to West Bromwich Albion, Everton and Newcastle United but 39-year-old Scholes, who won the Champions League twice with United, believes the manager has been unfortunate with injuries.
Dutch striker Robin van Persie, who scored a hat-trick in Wednesday's win, has missed big parts of the campaign and also exited on a stretcher with a leg issue before the end of the Olympiakos win.
"He's had a lot of injuries to cope with so I feel quite sorry for him," added Scholes, 11-times a Premier League winner who made 718 appearances for United before retiring last year along with manager Alex Ferguson.
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- Premier League