Lukaku, 23, is rumoured to be a man in demand after netting 25 goals for the Toffees this season.
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Roger Lukaku said in Het Nieuwsblad that he expected a transfer to have been completed before the start of the European Championships next month.
“At the moment I think Manchester United or Bayern Munich are the most suitable for him, especially Bayern,” Lukaku Sr said. “Every year they play at least in the semi-finals of the [Uefa] Champions League and the Bundesliga will suit him tremendously.
“He cannot go to Italy because they keep things closed at the back and it is too hard for an attacker. What is certain, to continue to make progress, he needs to change clubs, but we are mainly engaged in making the right choice.”
Lukaku Sr backed his son’s agent, Mino Raiola, to help the striker make the right decision for his future.
“Romelu will help determine the choice, but the agent usually has the last word,” Lukaku Sr said. “I hope, and think, Mino is fair, and that he is acting in the interest of the player. Now, with Romelu, it will be quickly arranged. I think it will be in order before the European Championships.”
Lukaku joined Everton initially on a season-long loan from Chelsea in September 2013. The move was made permanent the following summer, with the Toffees splashing out a club-record fee of £28 million (Dh148.3m).
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