Rooney, now 28, scored his first goals for the Goodison Park club at the age of just 16, before moving to Manchester United for £30m and netting a hat-trick against Fenerbahce as an 18-year-old debutante.
Barkley's breakthrough has been less dramatic, but Martinez insists that the 20-year-old is the "best young England talent" that he has ever seen.
When then asked: "Better than Rooney?", the Spaniard responded: "For me, yes."
Barkley, who has been capped three times by England at senior international level, has made 34 first-team appearances for Everton this season, scoring six goals in the process.