Koulibaly has also been linked with Tottenham and Arsenal, but it is claimed that United have moved quickly to land the defender.
The 28-year-old is however not expected to join until the summer
Italian journalist Fabio Santini broke the news, and speaking on the TV show Il Processo he said: “Napoli will sell Kalidou Koulibaly to Manchester United for a figure of around 70-75m euros. It seems all done.
“Naturally, such a deal will be closed only in June and certainly not in January in the winter transfer window.”
The signing would be the second time within a year United have spent big money on a centre-back, after Harry Maguire joined from Leicester City for £80m last summer.
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