Kane, 24, has claimed the Golden Boot in the past two Premier League seasons, while he took his tally for England to 10 goals with a brace against Malta on Friday.
Van Nistelrooy, who starred for United and Madrid during his career, hailed Kane, talking up the forward's performances and leadership.
"Harry Kane to me looks like a great professional, somebody who works hard to get the maximum out of himself. He shows that out on the pitch," the Dutchman told the Mirror.
"I think for Spurs he is a great player, a leader as well. That also goes for England. Added to that of course he is a great goalscorer.
"He is a true No.9 – a strong and forceful centre-forward who is always a reference point during the build-up play."
Kane's brace against Malta helped England retain their two-point lead atop Group F in World Cup qualifying ahead of a crucial clash against second-placed Slovakia on Monday.
So impressed by Kane's leadership, Van Nistelrooy said he would happily make him England captain.
"Nothing seems to faze Harry Kane," he said.
"He takes everything in his stride. I hear he is very popular with the other players and I wouldn't hesitate to make him captain."