Barkley has not played once this season, as he has been out with injury, and his future at Goodison Park is very uncertain.
However, Neville still believes that Barkley should start for England during their first match in Russia.
England booked their place at the World Cup this week, but their performances against Slovenia and Lithuania were uninspiring.
Tottenham’s Dier was one of the players who received the most criticism for his displays, as many felt he was too negative in possession.
Barkley, on the other hand, is a player who does try and play forward - and Neville has always spoken very highly of his former teammate at Goodison Park.
Despite Neville’s wishes, Tottenham’s Dier looks a far more likely pick for Gareth Southgate than Barkley does at this moment in time.