The 30-year-old suffered cruciate ligament damage against Basel in December, ruling him out for the season, but the Serbian is convinced that his Old Trafford teammates can secure the club's 20th league title.
"If you look at our history and commitment, you know we like to win all trophies and I believe we are the team in Manchester who will keep doing that every year," Vidic told The Mirror.
"Of course we're confident. We're challenging for the title and we're only three points behind City. We've had problems with injuries, but I think against Arsenal this weekend we have a good chance.
"It's good for the city of Manchester to have two football teams doing well. There's a lot of talk and banter."
Vidic joined United from Spartak Moscow in 2006.