Off contract in June, Van Dijk says developments are likely to accelerate closer to the end of the season.
He told Sky Sports: "In the next few months there will be updates on my future. When there is a definitive answer on my future, it will probably be made public... I have always said that I am quite calm about this."
He added: "I can't talk about the negotiations with the club about the contract, but I can only say that I am fully committed to Liverpool. I love the fans... let's see what the future holds. As long as I am calm, I think the rest of the world can remain calm.
"I am very well physically, mentally, and the only goal I have at the moment is to try to be successful with Liverpool. I want to be the best captain and player I can be for the team and the club."