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Neither club officially gave details of the transfer, but a source from Lille who was familiar with the transfer told AFP that the Ligue 1 team would receive 70 million euros ($82.8 million) with add-ons potentially worth 10 million euros.
Italian media report however that Napoli have shelled out 50 million euros before add-ons. Either figure would be a club record transfer fee paid by Napoli.
Osimhen, 21, scored 18 times last season and was one of the revelations of France's curtailed campaign.
Napoli go into their final match of the season against Lazio knowing they will finish seventh in Serie A. They have qualified for the group stage of the Europa League by virtue of winning the Italian Cup.
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