According to Corriere dello Sport (via the Metro), United are finalising preparations and will bid for Koulibaly soon.
Ole Gunnar Solskjaer is reportedly desperate to sign a top centre-back to bolster a leaky defence.
United's proposed bid would be £84 million, which would make Koulibaly the most expensive defender in history.
However, with Koulibaly's release clause sitting at £133 million, Napoli are thought to be hanging on for a fee closer to that figure.
If the Reds fail in their pursuit, they will focus on other targets such as Ajax's Matthijs de Ligt and Leicester's Harry Maguire.
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