After consulting with surgeons, it was decided Lukaku's best recovery option was "conservative therapy", which will see him out of action for "three to four months".
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Both Lukaku and Napoli management are in agreement over the decision.
The Belgium centre-forward suffered the injury in preseason action against Olympiakos last week.
Napoli management have also decided against registering Lukaku for the Champions League group phase over the first-half of the season.