United have endured a miserable season and manager David Moyes paid the price when he was sacked last month.
The Premier League champions are seventh in the table and look set to miss out on even a place in the Europa League next season.
Moyes was dismissed just 10 months after replacing Alex Ferguson at the helm and Netherlands coach Louis van Gaal is widely expected to arrive at Old Trafford to take over from interim boss Ryan Giggs.
Inter-bound centre-back Vidic is backing United to come good again under new management.
"The foundations are here," the defender told United Review . "The club is structured well.
"The manager who comes in should be relaxed about the people around him as he will have help from whoever he asks.
"There are not people who will try to throw things his way, they will always be helpful and that is a great thing for the manager to have, whoever he is.
"I think he has a great base to achieve something big and I hope he is going to step up next year so United play an important role in English football again."
Vidic joined United in 2006 from Spartak Moscow and has gone on to make 299 appearances for the club, scoring 21 goals and taking the captain's armband from Gary Neville in 2009.
