Rooney, a former England captain himself, admits he's a big fan of the former West Ham skipper.
"For me, he's the one who's probably waiting for Harry to hang up his boots at some point," Rooney said in the latest episode of BBC Sport's The Wayne Rooney Show.
"He was all over the pitch (against Everton). His decision-making – when to pass it, where to pass it, what foot to pass it to, his detail on his pass – it was a pleasure to watch. He was absolutely incredible.
"He was splitting centre-backs, taking the ball off (Arsenal's) centre-backs, acting as a third centre-back, then next minute he's in the box, trying to score a goal. Sometimes, some of the stuff he does is a bit underrated.
"He's the right one to take over (Kane) for me, because (of) his drive, his personality. Everyone seems to love him, who knows him, who's close to him. He's irreplaceable for England."