The Netherlands centre half is out of contract with the Anfield club in the summer.
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While Van Dijk would love to stay at Liverpool, he admitted that he was only thinking about their next Premier League game against Manchester City.
"What a direct question from you! They don’t ask me that direct," he told Spanish outlet El Chiringuito after Liverpool's 2-0 win over Real Madrid in the Champions League.
"But listen, there is, at the moment, nothing I can say. The only thing that I can say is I’m fully focused on Man City from now on."
Van Dijk was then pushed over whether he could join Real Madrid.
He added: "Do they? I don’t know (need a centre back).”
When pushed again, he added: "But (Antonio) Rudiger is there, no?”