Van Dijk, 25, has been heavily linked with a move away from Southampton this summer with Arsenal, Liverpool, Chelsea and Manchester City all apparently interested in securing his signature.
The Dutch international has been a standout performer for Saints throughout this season.
He was rewarded with a new six-year deal last summer and club chairman Ralph Krueger claimed last month they are prepared to turn down £60m bids for their star man.
But The Daily Mirror claim Saints have upped the ante in their bid to keep hold of Van Dijk by ramping up his asking price to £70m.
Virgil van Dijk's next club: Where could the Southampton star go next? Tue, May 9, 2017
Where could Southampton star Virgil van Dijk go next? Odds provided by 888sport
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Which clubs are tipped to sign Virgil van Dijk? Odds provided by 888sport
It is claimed Manchester City are one of the frontrunners in the pursuit of his signature with Pep Guardiola keen to hand him a huge £180-000-a-week deal.
But Liverpool boss Jurgen Klopp is aiming to better this offer by handing him a £200,000-a-week contract.
Arsenal boss Arsene Wenger wants to sign two marquee players as he bids to kick start a new era at the Emirates after signing fresh terms with the club.
Southampton have slapped a £70m price tag on Virgil van Dijk.
While Chelsea boss Antonio Conte wants to improve his squad to be able to cope with the demands of both defending the Premier League title and playing Champions League football next season.
Southampton have become a selling club in recent seasons, but owner Katharina Liebherr is keen to shake this off.
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Krueger said: “We do not need to sell any players. Whether the ownership changes or not, it is not going to change our strategic position.
“We have the backing of Katharina and/or any potential change which we as a management team feel extremely comfortable with.
Southampton are demanding potential suitors pay a huge £70m for Virgil van Dijk
“We have a strategy which is being fine-tuned, but the base is in place.
"We are pre-positioned for the transfer window and we do not have to sell any player. That will be our decision and whether it is in the best interests of the club or not.”
Van Dijk is currently recovering from an ankle injury after missing the last four months of the season.