The Belgium international midfielder has struggled to recreate the form he showed at Goodison Park in his five seasons with Everton since he followed David Moyes to United, where Fellaini is awaiting his first goal for the club.
Neville, though, is not concerned about the 26-year-old's form and believes he will only get better for United as the duo, along with manager Moyes, prepare to welcome their former club Everton to Old Trafford on Wednesday.
"We are really relaxed and we are really patient with Felli (Fellaini) because you have seen it with players in the past like Patrice Evra and Nemanja Vidic. It took them six months to settle in here," he told the Manchester Evening News.
"It is not just the games on a Saturday or midweek, it is the intensity of the training, the size of the club and the expectation from the fans.
"All the other things like that that go with playing for Man United, it takes time to get used to. As the games keep going on, he will just get better and better."
And former Everton captain Neville thinks Fellaini's confidence will begin to grow when he produces match-winning performances for the team.
"What is important for Marouane now is to play well in a match that we win and he scores a goal," he added.
"He needs to score and win. That is the next step for him.
"The United fans haven’t seen the best of Marouane Fellaini."
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
