The Azzurri are keen to wrap up any business for the defender earlier in the transfer window.
That’s because they need to sell a few players in order to make funds available for new purchases, it’s claimed.
But, Koulibaly is currently on international duty with Senegal, ahead of the 2019 Africa Cup of Nations.
Senegal’s first match is against Tanzania on June 23 in Cairo, Egypt.
United had reportedly been readying an £84m bid for Koulibaly earlier this month.
Solskjaer had hoped that Koulibaly would be the face of his new-look United squad.
Juventus are also lurking in the background, with Maurizio Sarri making the defender his number one priority this summer.
Sarri has a good working relationship with Koulibaly from his time at Napoli, and that could persuade him to move to Turin.
PSG could also make a move for the in-demand centre-back, if they fail to land Dutch wonder kid Matthijs de Ligt.
But, the Parisians would struggle to pay more than €100m for Koulibaly, especially after its previous exploits in the transfer market, according to reports.
Meanwhile, Liverpool have been given the green light to sign Barcelona forward Ousmane Dembele this summer.
Anfield is believed to be the Frenchman’s preferred destination, and the deal would allow Barcelona to progress in their pursuit of Antoine Griezmann.