Club president Zdravko Mamic confirmed he turned down an offer for the central defender after meeting Hoops chief executive Peter Lawwell, who was in Zagreb for talks, but could not seal an agreement.
Celtic must decide on whether or not to make an improved offer for Simunovic, a deal revealed by CQN on Saturday.
Southampton are confident of landing the Dutch ace, but Celtic boss Ronny Deila is hoping the player may stay with the incentive being the chance to experience the Champions League group stages.
And the manager is not convinced tonight’s Malmo clash will be a last outing for van Dijk in front of the Hoops fans.
On the speculation that Van Dijk will shortly leave the club, Deila said: “I wouldn’t say that. We’re in control and he’s a Celtic player who still has a long contract here. I hope we can have him longer than these European games.”
Deila also issued a vote of confidence in Dedryck Boyata after his errors gifted Inverness Caley Thistle two goals in the 4-2 weekend win.
He said: “Dedryck was one of our best players against Qarabag. People are talking about the game against Inverness, but that’s just two things.
“It can happen to anyone. I wouldn’t swap our two central defenders with many players in the world.”