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The former England midfielder won the last of his 66 caps in Euro 2004 when an 18-year-old Rooney scored four goals.
And Scholes, who was also a Manchester United teammate of Rooney, Barkley's performances in England's recent friendlies convinced him that the 20-year-old has to start for his country.
"I was watching the England-Ecuador friendly in an airport lounge, a bit back from the screen," he wrote in his Paddy Power blog.
"In the first half Ross went on a run and I thought: 'Bloody hell, is that Rooney?' Barkley made me think of Wayne at Euro 2004. I had to take a second look because I thought it was Wayne."
Scholes also hopes to see plenty of Liverpool teenager Raheem Sterling and selected both in his England side, at the expense of Jordan Henderson and Adam Lallana.
"Now is a great chance for Roy Hodgson to give English football the identity we've lacked," he added.
"Tell the world: this is how we play, attack! There is no point taking people like Raheem Sterling or Ross Barkley to Brazil 'for the experience'. Play them.
"Some people might say it's risky. But these players have the fitness and ability to get the ball back if they lose it (hopefully not in dangerous positions). You want them to attack and give the opposition problems.
"Roy Hodgson has little to lose by going for the jugular. Will we be satisfied if England scrape through to the quarter-finals playing negative football?
"Let's not do that and take responsibility for what happens if we go for it. Let these England players off the leash. Let's give them something to worry about. Ross Barkley must start."