It's been reported the Uruguay defender was finalising a move on Thursday.
“Godin is a player who needs no introduction and therefore isn't just of interest to us, but to many clubs," Cagliari director of sport Carta said.
“There was an approach with him and his entourage.
"The player wants to join us, but clearly the negotiations are not easy. We're in the early stages, but if the conditions were to be right, then it'd be a big opportunity for us in terms of leadership and experience."