Chamberlain arrived from Southampton last summer for a hefty price tag but has impressed spectators and pundits alike with the maturity of his game for one so young.
The 18-year-old has put in a number of eye-catching performances, including the 3-0 win over AC Milan, which have led to comparisons between himself and Rooney when he was a teenager.
Arsenal manager Arsene Wenger has already stated his belief that Chamberlain will have the same effect as the Manchester United striker did when he was just 18, and be selected for England's Euro 2012 squad.
Now Van Persie has told The Sun on Sunday: “Alex can have a big impact. He has everything you need, I'm sure he has a bright future for Arsenal and England.
"He's shown that already in a couple of games. He has pace, he is clever, knows when to pass, when to keep the ball and has good technique.
“He's a bit like Rooney, who I rate highly. Rooney's a big player and a good all-rounder who can score goals, provide assists and make nice runs — he has a bit of everything.
"And although Alex plays on the left or right — whereas Rooney plays more through the middle — that could change in the future. They are both good all-round players."