The Dutchman is out of contract in the summer, but the club are hopeful he will extend his stay.
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Van Dijk, who helped his team to a 2-1 win over Chelsea at the weekend, admitted that contract talks were underway.
"Discussions are ongoing, we will see what happens in the future," said Netherlands center-back Van Dijk.
"My full focus is on Liverpool, wanting to win games that are ahead of me and nothing else.
"What the future will bring I have no idea at the moment. I can only tell you that discussions have started and we will see."