And according to Santini, United have reached an agreement between £60m and £64m.
Solskjaer’s current defensive options are Harry Maguire, Victor Lindelof, Phil Jones, Marcos Rojo and Axel Tuanzebe.
Rojo and Jones are both expected to leave United in the summer and Koulibaly would be a major upgrade on both.
Earlier this month Solskjaer confirmed he was looking to add experience to his side.
“That’s something that we’ve spoken about in this room a few times; that we are a young team,” said the manager.