Liverpool are expected to reignite their interest in Van Dijk once the transfer window reopens in the New Year.
Jurgen Klopp's side have come under heavy scrutiny this season for too many lapses in concentration at the back.
Dejan Lovren has in particular come in for strong fodboldtrøjer
criticism for individual errors.
Liverpool failed to strengthen their options at centre-back in the summer as Klopp had no back-up option for Van Dijk.
But Southampton boss Pellegrino admits he can't be certain whether the Holland international will remain a Saints player after January.
'I don't know. I can't control the market,” Pellegrino admitted.
“You never know, because when we talk about money everybody has got a price.
“The budget is to sign players and the biggest teams have got money to try to sign players.
'I can't decide about that. This is a fodbold trøjer
question for our owners.
“Everybody is focused on their area, to try to bring the best players possible for their club. It is something that happens every single transfer window.
“We have got a lot of good players and most of the teams want to sign them.”
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