Barkley, 20, has six England caps and has impressed in the recent warm-up matches as the Everton man has looked to inject speed and excitement into Hodgson's side.
It remains to be seen if he will feature from the start in England's World Cup opener against Italy on Saturday night but Scholes, who suggested recently that Rooney may have past his peak, believes Barkley is now in a place where the Manchester United forward was leading into Euro 2004.
"I was watching the England vs 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."
An 18-year-old Rooney burst onto the international scene by scoring four goals at the European Championship a decade ago but is still yet to find the back of the net during the World Cup finals.
Scholes wants to see England attack in Brazil, with flair players like Barkley and Liverpool's Raheem Sterling now taking centre stage.
"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."