The Red Devils failed to progress into the quarter-finals of the elite tournament in last term's campaign following a controversial defeat to Real Madrid.
Despite new manager David Moyes's lack of experience in Europe, Vidic believes that with a bit of luck, the Premier League champions could have a successful campaign.
"It's not something easy," Vidic told talkSPORT. "Any team in the world can say, 'we want to win the Champions League'.
"We have a target, and that's why we prepare hard. We think we can go to the later stages and with a bit of luck, yeah, we can win the tournament."
United have been drawn Bayer Leverkusen, Real Sociedad and Shakhtar Donetsk in the group phase, with their first match against Leverkusen due to get underway next Tuesday.