Unsworth is in temporary charge of Everton at the moment, having been placed in his current role following the departure of Ronald Koeman.
Former United and Everton star Neville has suggested two reasons why the 44-year-old former defender should be handed the Goodison Park role.
"One, I think he's a good person,” Neville told Sky Sports about Unsworth. “Two, he's done his hard graft in the youth team and the U23s, I hope as a young English coach he gets an opportunity to do well.”
Unsworth has won one and lost three of the four matches he has been in charge of the Everton first team at the moment.
It is too early to judge whether the Englishman is good or bad for Everton for the rest of the season.
However, it would make sense for the Merseyside outfit to appoint someone who has extensive managerial experience.