The centre-back is heading into the final months of his contract with the Reds alongside Mohamed Salah and Trent Alexander-Arnold.
Van Dijk, who is club captain at Anfield, revealed in October that discussions over a new deal are 'ongoing' and reports on Thursday even suggested he has agreed to extend his stay.
However, talkSPORT understands these rumours are wide of the mark and the defender's future remains unresolved, with an El Chiringuito journalist taking the opportunity to seek clarity from him.
"Your future, will you stay here?" he asked Van Dijk after Liverpool's 2-0 Champions League win over Real Madrid on Wednesday night.
"What a direct question from you, they don't ask me that direct!" the defender said in response, seemingly surprised by the journalist's forwardness.
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"But listen, there is, at the moment, nothing I can say. The only thing I can say is that I'm fully focussed on Man City [who Liverpool play on Sunday] from now on."
The journalist then hinted at the possibility of him joining Madrid if he was to leave Liverpool, saying: "Real Madrid needs centre-backs."
"Do they? I don't know," Van Dijk replied before being told that fellow centre-backs Eder Militao and David Alaba are injured at Madrid.
"But [Antonio] Rudiger is there," the Liverpool star insisted, although the journalist returned by asking: "Maybe you go to Madrid?"
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Van Dijk diverted again, responding: "When? In the summer? Like I said before, the main focus at the moment for me is Man City."
It's clear the weekend showdown is his main focus at the moment, as Liverpool look to open up their gap at the Premier League summit and pile further misery on their regular title rivals.
Van Dijk is set to play a major role in the match and will know that a Reds win could see them extend their lead at the top to 11 points - over a Man City side that has not won in six games, having lost five of them.
However, with the Dutch international available to speak to foreign clubs over a pre-contract agreement in January, questions over his future are likely to stick around.
The 33-year-old has been a pivotal part of Liverpool's success since signing from Southampton in 2018.
Van Dijk has totalled 287 appearances in all competitions, winning trophies including the Premier League and Champions League.
He played the full 90 minutes of the dominant win over Madrid on Wednesday night to sustain their 100 per cent record in Europe's elite competition, where they also top the table.
Alexis Mac Allister and Cody Gakpo were the scorers for Arne Slot's side in a match that saw Salah and Kylian Mbappe miss penalties.