The Nigeria international has attracted enquiries from Arsenal in recent days, while Newcastle failed with an €80m offer in January.
Today, La Repubblica says United have now tabled a €100m cash offer for Osimhen.
Napoli president Aurelio de Laurentiis has the deal in front of him and is today scheduling a meeting with the player's agents to discuss the move.
For his part, Osimhen has ambitions of playing in the Premier League, though United's lack of Champions League football could be an issue.
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