Rooney has returned to his boyhood club Everton and is in the best position to pass on tips on how to follow in his illustrious footsteps.
And he believes Lukaku, who last week moved from the Toffees to United for £75million, has got to bring mental strength to his undoubted physical attributes.
Rooney said: “Playing for Manchester United is a test of character as well as your ability. You have got to be strong enough mentally to accept the challenge.
“United are a football club which demands success. Romelu has to be strong enough to take up that challenge. If he does that, then with the ability he’s got he will be a success. If he doesn't, if he worries about things, then it will be more difficult."
Wayne Rooney hopes Romelu Lukaku is ready to handle the pressure at Manchester United
Wayne Rooney has now moved back to his boyhood club Everton
Playing for Manchester United is a test of character as well as your ability
Rooney knows all about living in the pressure cooker world of United and will be forever grateful for the guidance given on how to handle it.
United boss Sir Alex Ferguson never let him forget the high standards to be met, and Ryan Giggs, Gary Neville and Paul Scholes were always around to dish out advice.
Rooney added: “There are standards that you have to keep when you are at Manchester United. That obviously came from the manager, Sir Alex, when I went to United.
“And it was passed down by the likes of Giggsy, Gary and Scholesey. Over the last few years it was down to me and Michael Carrick to keep the new players maintaining standards.
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Romelu Lukaku in Manchester United's first training session Mon, July 10, 2017
Click to reveal the best snaps of Romelu Lukaku in Manchester United's first training session of the season
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Romelu Lukaku got stuck into Man Utd's first training session of pre-season
“That has been more difficult over the last few years with some of the players who joined the club. But that’s not my problem anymore. I’m just ecstatic to be back at Everton.
“I need to get in the dressing room and learn about the players here. I think we’ve got a good group. I’ve played with a few of the lads at club and international level.
“There are also some young lads. It’s a good mix and I’ll be trying to help the young lads to get the best out of them.”
Rooney’s Goodison return is, as he says, not an entry into a retirement home.
Romelu Lukaku completed his £75m move to Manchester United last week
He’s there try to turn the club he’s loved from being a toddler into winners.
He could have stayed at United and collected his money from the bench. And there were bigger weekly wage packets on offer than his current £125,000.
He said: “I am not that kind of person. I don’t just want to play and not care whether you win a trophy or not. Ronald Koeman and the club have shown me that ambition about where they want to go to and it was perfect for me to come back.”