Kane, 21, has been drafted into the England squad by manager Roy Hodgson after scoring 29 goals this season and could make his debut in Friday's 2016 European Championship qualifier at home to Lithuania.
It is over 12 years since Rooney made his England debut at the age of 17, in a friendly against Australia at Upton Park, and he has encouraged Kane to relish every second of his international career.
"When you're playing for your country, the one thing you want to do is enjoy it," Rooney told journalists at the England team hotel in Watford, north of London on Thursday.
"And listen to your friends and family and coaches, because if you start listening to people from the outside or reading too much of what is in the press about how good you want to be or how well you did or didn't do, it does affect your mind.
"So enjoy it and keep doing what he's doing, concentrate on his football. I'm sure he'll have a good career if he does that. It took me a few years (to realise that)."
Hodgson refused to reveal whether Kane would start against Lithuania, but Rooney predicted that the youngster would face a nervous night's sleep regardless.
"He'll be lying in bed tonight (Thursday) hoping that he'll make his England debut tomorrow," said Rooney, who described Kane's recent displays as "sizzling".
"I can imagine that. I know because I've felt the same feeling, the excitement he'll have tonight."
A sell-out crowd of 90,000 is expected at Wembley, but Hodgson believes Kane will be able to handle the attention.
"I would like to think he is up to the expectations," said the England manager, whose side are seeking a fifth successive victory in Group E.
"If he is going to be a top England player as we hope he will be, then I suppose you have got to learn to deal with these expectations.
"Wayne Rooney, if I remember, thrust in against Turkey in a vitally important game (a Euro 2004 qualifier in April 2003), came out not only smelling of roses, but he is sitting here with 101 caps.
"But there are other examples. I am pretty sure you (reporters) can give me another example of someone who in a similar situation got thrown in and turned out to be disastrous. But we believe in Harry."
A hip injury to Liverpool's Daniel Sturridge appears to have opened the door for Kane, but Arsenal's Danny Welbeck is also in contention to partner Rooney in attack.
Michael Carrick, meanwhile, is expected to step in for the injured Jack Wilshere at the base of England's midfield diamond.
Igoris Pankratjevas's Lithuania, currently ranked 94th in the world, won their first two qualifying games, against San Marino and Estonia, but have since lost 2-0 at home to Slovenia and 4-0 away to Switzerland.
"We are quite realistic about it," Pankratjevas told his pre-game press conference.
"We are not dreamers. It is always history that Lithuania are playing England for the first time ever.
"Obviously none of the players have played at such a stage, so we are preparing them mentally for this kind of game.
"I like the England team in general recently as they have some new players along with their experienced ones."
Lithuania will be missing former Hearts winger Arvydas Novikovas and striker Lukas Spalvis due to injury, but right-sided midfielder Fedor Cernych is fit following a foot problem.
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