Lukaku has turned down a contract extension at Goodison Park, with agent Mino Raiola claiming this week that Everton have promised their star man he can leave for "certain clubs".
His former team Chelsea have been heavily linked and Courtois would welcome the 24-year-old back at Stamford Bridge.
"Romelu is a great player so if he decides to go to Chelsea or Chelsea decide to sign him, I would be happy to see him in the dressing room in July," the goalkeeper told Sky Sports.
"I guess if it's the right offer he might go. It's up to him to decide."
I want to thank my teammates and the staff for helping me this season! To the fans thank you for your amazing support God bless you pic.twitter.com/FV22vJoCex— R.Lukaku Bolingoli10 (@RomeluLukaku9) May 9, 2017
Meanwhile, Courtois is keen to commit his own future to Chelsea, where he is waiting on a new contract offer.
"I am very happy and there is no doubt I will stay," he said. "My contract runs out in two years so, obviously, I need a new deal.
"It's important I finish the season well with the national team and then maybe Chelsea will speak with my agent. If it's a good deal I will be very happy to sign."