The Serbia center back has returned to the first team after eight months out claiming his knee is in "perfect condition."
Vidic suffered the blow against FC Basel in December and missed the rest of last season, but says now that he has returned he is ready to be reunited with the England center back.
The duo formed a formidable partnership that helped United to Champions League glory in 2008 and the Serbia international sees no reason why they cannot return to that level.
"I have no doubt Rio and me can again be the best couple of central defenders in the Premier League," Vidic told ESPN. "That's the way it has been for a few years and now my dream is for us to return to the same level. People can think anything they like. But, all things being equal, it is very difficult for anybody to get the better of us.
"My knee is in perfect condition. My only challenge this season is to avoid more injury. I'm still not 100 percent, but this will come with more minutes on the field and more hard work. I've received a lot of confidence from the manager and this is the main thing for me."
Young defenders such as Chris Smalling and Phil Jones stepped in in Vidic's absence and the 30-year-old predicted that the club's trophyless campaign would motivate it to do better both domestically and in Europe during the 2012-13 season.
"We had some young players play a lot of games last season," he continued. "They'll have learned a lot. We all learned. In Europe we've had so much success in recent years and maybe relaxed a bit. We were punished and can't allow that to happen again.
"We had a few injuries last season too. I hope everyone can stay fit this time. To lose the league title was hard for us but is forgotten now and we are only thinking of becoming the owners of the English championship again."
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