The Belgium international, who will feature for Jose Mourinho's side this season after a successful loan spell at West Brom, would welcome the 27-year-old "with open arms"
Jose Mourinho has made the club's intention to sign Rooney clear this summer, while the Belgian is also part of the Stamford Bridge boss' plans for this season after a successful loan spell with West Brom.
And Lukaku is already relishing the potential challenge of more competition for places in the form of the Manchester United striker next season.
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"I like competition. Obviously, if he does sign, it could be a good partnership but it is the manager's choice.
"You have to accept that you have to work hard to make it a successful squad. If he is part of our team I will welcome him with open arms."
Lukaku, meanwhile, has been impressed by Mourinho's approach as he works with the former Real Madrid coach for the first time.
He added: "He is a great manager. He is very direct - and I love that. If he has something to say to you, he says it. That is a good thing.
"I would not say he has given me a hard time but he is very direct and in your face. I have had to work more than I ever have but I like to work."