Corriere dello Sport claim the Italian club "immediately" rejected the world-record offer.
Jose Mourinho's desperate search for a quality defender saw United up their initial £77m offer by £14m.
The Old Trafford boss was furious at the club's failure to sign a new defender in the summer after botched moves for Harry Maguire and Toby Alderweireld.
In September, he claimed his defenders were not good enough to compete for the Premier League title.
Chris Smalling and Victor Lindelof have become Mourinho's first-choice partnership of late but Mourinho is eyeing a number of targets to improve his back line.
Koulibaly, 27, is one of just two players in Europe to have played every minute of football so far this season.
Napoli have conceded just 13 Serie A goals with the Senegal international in the team this season – the fourth best record in the league.
And club president Aurelio De Laurentiis' refusal to sell a player bought for just £7m from Genk in 2014 for a staggering £84m profit highlights how important he is to the side.
Chelsea, Liverpool and Real Madrid have all previously been linked with a move for Koulibaly.
Mourinho will be hoping to sign Koulibaly as part of an incredible defensive overhaul to raise money for new recruits.
Eric Bailly is set for talks over his Manchester United future — just two years after his £30million switch from Villarreal.
The Ivory Coast ace, 24, has not started a game since boss Jose Mourinho subbed him before half-time against Newcastle last month.
He is available on a free transfer next summer and looks set to be cut loose in order to free up room for new faces.
Meanwhile, Marcos Rojo is reportedly closing in on a move to Premier League new boys Wolves, while Matteo Darmian could be on his way to Roma.
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