The Reds manager is keen to bolster his backline following a shaky start to the season and the Napoli ace appears to fit the bill.
United face losing a number of their defenders in the near future and Mourinho has no choice but to find backup.
But he is one of the many managers in Europe that are keeping a close eye on the Senegalese star.
Koulibaly has been also been linked to Premier League rivals Arsenal and Chelsea this season, but Napoli don't want to get rid.
The Italians pinned the 27-year-old down with a new five-year deal in August and he has been slapped with an £80million price-tag.
But Mourinho will have to be willing to fork out in the upcoming transfer window if he wants to secure his top target.
His mission to sign Toby Alderweireld now looks unlikely after the Spurs defender opened the door to an emotional Ajax return.
United had been linked to Milan Skriniar, but Inter Milan have valued him at £100m which is likely to end the interest.
The Reds boss will need to bolster his defensive this time round following his underwhelming performance in the last transfer window.
With string of stars facing axe, how will United line up next year?
JOSE MOURINHO has taken every opportunity he can this season to moan about how unhappy he is with his defence.
Chris Smalling and Victor Lindelof have made the centre back slots their own but United still continue to ship goals.
Smalling could be on his way out to Everton, while Ashley Young, Marcus Rojo, Eric Bailly and Matteo Darmian are also thought to be close to the exit.
So with those lot going, who's coming in, and how will United line up next year?
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Koulibaly ticks every box following his sublime spell of form for the Serie A side, where he has made over 130 appearances since he joined in 2014.
And the The Times have suggested that the central defender would be open for a move to the Premier League.
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