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However, the German warned the Dutch would be unwise to rush back their captain after so long out.
Van Dijk has not played since suffering a serious knee injury in the Merseyside derby draw with Everton in October last year.
Netherlands boss Frank de Boer had previously said he would not be counting on van Dijk’s fitness for the summer tournament.
But this week the centre-back shared footage of himself back running on grass at Liverpool’s training ground, sparking speculation he could be set for a surprise early return ahead of the Euros.
While Klopp poured cold water on the idea of an imminent return, he vowed not to stand in van Dijk’s way - if he is truly fit.
“Virgil’s knee. I don’t want to hold him back, but you can’t force it as well,” Klopp said.
“You can’t after 10-11 months out, train a week and play football. That’s just not possible, it shouldn’t be possible.
“Nobody holds him back, I can promise all the people in the Netherlands or wherever. But we can’t force it as well and we’ll not. We speak about a player and his career.”
Van Dijk is yet to return to full training with Liverpool but is making steady progress.
“He just tries to get fit as quick as possible,” Klopp said.
“In the moment, nobody knows when that (his return) will be exactly but you can imagine it’ll be tight with the Euros ... because he’s not in team training yet and will not be in the next weeks. So, I don’t know.
“But in the end it’s the decision of Virgil and he’ll get massively influenced by the feeling in his knee.”