United finished outside of the European places this season after a torrid time for David Moyes at the helm but Louis van Gaal is set to be named the new boss at the start of next week.
Neville was appointed coach under Moyes after retiring from football last season and has stayed around to help out Ryan Giggs in his caretaker role.
Neville’s future is unclear but the future of his club is rosy according to the former England man.
“The target is to win the Premier League back again and definitely qualify for the Champions League,” Neville said.
“Some clubs just aim to be in the Champions League but I don’t think that’s good enough for Manchester United.
“I think we have to continue to win trophies because we have been so dominant over the last 20 years. We need to make sure we get back up to those levels of performance and consistency.”