United made an early start to their summer recruitment drive two weeks ago when they signed Depay from PSV Eindhoven for £25million.
With the Dutch season now over, Depay is free to complete his transfer to the 20-time English champions and a medical was reported to be under way on Monday.
Depay was the Eredivisie's top scorer this season, scoring 22 goals in 30 appearances.
But given that he is just 21 years old, Neville thinks it may take time for the winger to blossom into the world-class player he hopes to become.
"It's a typical Manchester United signing to sign someone who has got potential but hasn't yet grown to become the finished product," the former United captain told Sky Sports.
"United have done that over the years, particularly with foreign players.
"I think Depay looks like an exciting player but there's a lot of obstacles to overcome to determine as to whether he going to become the real deal.
"He's got to settle in the country and get used to playing football in Manchester
It will be different but it fits the bill in terms of him being a young player."
Manager Louis van Gaal gave a similar assessment of Depay when writing in his programme notes for Sunday's 1-1 draw against Arsenal.
Van Gaal handed Depay his international debut in October 2013 and took him to the World Cup the following summer, where he scored twice in four appearances for Holland.
"I have worked with Memphis during last summer's World Cup with the Netherlands and he has great potential," Van Gaal wrote.
"The plan is to help him develop as a player, but we must all be patient.
"The Premier League is very different from any other league and it will take time for him to fully adapt to the pace and unforgiving nature of football in this country."
Source : PA
Source: PA