The 21-year old Dutch defender is set to join the Hoops from FC Groningen according to SunSport.
It is believed that Celtic will pay the Dutch outfit £2.5million for van Dijk's services but director of football Hans Nijsland says there are a few payment demands to be agreed upon.
"The deal is not yet complete, but we are getting close. I'm just waiting for a call from the big boss at Celtic," he said.
"Moving to a fantastic club with Celtic's great history is a great opportunity for Virgil. It's clear he is ready for the next step in his progress.
"But we view him as one of the best defenders in Dutch football and we want to get the best deal for our club.
"However while the deal has to be right, there has been good co-operation between us."