Barkley's Everton contract expires at the end of the 2017-18 season and his failure to agree a new deal at Goodison Park has led to suggestions Tottenham, Chelsea or Manchester United will attempt to lure him away from Merseyside.
Barkley started one game and came off the bench twice for Hodgson's England team at the 2014 World Cup but failed to make an appearance at Euro 2016.
Hodgson, speaking about the development of young footballers at the Leaders Sport Business Summit in Beijing, said: "If Ross can find a club where people believe in him as much as we did in the England set-up he will do well.
"With us he faced strict competition. He didn't not play because we didn't think he was good enough.
"He's a risky passer, a midfielder who will turn with the ball, take players on and attempt a shot from 20 yards.
"Some of the 20-yard shots will fly over, some of the turns in midfield will be dispossessed and some of the risky passes will be cut out.
"But there are lots of players who can't produce that level of ability."
The uncertainty over Barkley's future prompted Everton manager Ronald Koeman to acknowledge he would look for new attacking midfielders, and the club signed Davy Klaassen from Ajax for £23.6million in June.
Barkley is set to miss the start of the new Premier League season with a groin injury, and, when asked if the 23-year-old was in danger of becoming a lost talent, Hodgson said: "Yes he is, because of the pressures we put on people.
"All of us, coaches, journalists and fans are intolerant of bad games and mistakes.
"He's definitely a talent. He'll win some games for his club and for England, too."
He added: "If he gets to a club where they buy him for what he can do and not what he can't do, someone will end up with a very good player."