Alexander-Arnold was part of England's World Cup squad during the summer and scored his first international goal in the recent friendly match against the United States.
But Barnes fears that Manchester City's Walker and Tottenham's Trippier will both remain ahead of the Liverpool favourite in the Three Lions setup.
"Alexander-Arnold has had a great start to the season, but for me Kyle Walker is a better player and will always remain first choice at right-back in the England team if they play with a back four," Barnes said, speaking exclusively for bookmaker comparison platform BonusCodeBets.co.uk.
"It's a pity he doesn't play on the left - Walker and Trippier will always keep Alexander-Arnold out of the England team."
Despite Barnes' declaration that Walker and Trippier are better, the ex-Liverpool number 10 claims that this current England side is not as talented as the 'Golden Generation' that briefly threatened to win Euro 2004 - a team containing stars such as David Beckham, Steven Gerrard, Frank Lampard, Paul Scholes, Ashley Cole, Michael Owen, Wayne Rooney and John Terry.
"This England team is not as good as the team from 2004 - the golden generation," Barnes said.
"People need to stop hyping this team up. There is great of potential there, but they are not ready yet."
Barnes thinks part of the problem is that not enough English players are being given chances by Premier League clubs. In that respect, Alexander-Arnold is a relatively rare exception.
"I'm worried about England's future. Younger players at Under-20 and Under-21 level are having to go abroad to get game time. Top Premier League clubs need to make a place for young English players," he commented.
"Top teams should be giving these players an opportunity, look at Phil Foden, he needs game-time but won't get it. Jadon Sancho has to travel to Dortmund, Reiss Nelson the same, having to go abroad. For every talented player that's willing to go abroad in search of game time, you've got another ten that won't leave England."
Source : 90min