The Dutchman centre-back has developed into one of the best defenders in the Premier League since joining from Celtic in 2015.
The 25-year-old is currently out with a foot injury but there is considerable interest in the player.
And the Telegraph say Chelsea boss Antonio Conte has set his sights on bringing Van Dijk to Stamford Bridge.
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Man City are said to be Chelsea’s most likely challengers for the defender.
Van Dijk would be a long-term replacement for John Terry, who appears unlikely to be given a new deal at the end of the season.
His arrival would also cast doubt on Kurt Zouma’s future, with the Frenchman unable to break back into the team after recovering from a long-term knee injury.
Southampton defender Virgil van Dijk
And Zouma, who is under contract with until 2019, says he will decide his future at the end of the camapign.
He told beIN SPORTS: "Leave Chelsea?
“We’ll see at the end of the season."