The former Everton captain discussed the duo during a quick Q + A.
Indeed, during a quick Q + A with fans on Twitter, the current Valencia assistant singled Barkley out when asked if there was one youngster he could always envisage success for.
The 21-year-old is now one of Everton's leading lights, while also playing a big part in England's recent qualifying campaign for Euro 2016.
Barkley has clearly developed into an able player for the Toffees but it's now about how far he can go. Attitude will be crucial, while the youngster needs to produce consistently, having been known to drop off for entire matches last season.
@fizzer18 name 1 youngster at Everton that you knew would be a star!— David Brown (@BrownDogg10) November 13, 2015
Meanwhile, Neville also reserved praise for another former team-mate on Twitter.
Asked who the most underrated player he has ever played with is, the former Everton man didn't hesitate before replying with Leon Osman's name.
@fizzer18 most underrated player you have played with ?— kevin sullivan (@kevin5886) November 13, 2015
The Goodison Park outfit host Aston Villa in their first Premier League clash after the international break and Roberto Martinez will no doubt hope for all three points there, despite Remi Garde earning an admirable 0-0 draw against Manchester City in his first game in charge of Villa.