The Southampton star has handed in a transfer request at St. Mary's.
Chelsea and Liverpool have registered interest in the Dutch defender, 26.
And according to the Daily Telegraph, the Blues are still desperate to land Van Dijk.
They say Chelsea will make a bid for the defender if Southampton are willing to sell and give the green light to the move.
The Blues reckon their approach will put themselves ahead of the pack who are eying Van Dijk.
The Telegraph add that Chelsea are willing to play the waiting game and could even hold off until next summer to land the Saints star.
Antonio Conte is keen to spend big this summer.
The Blues boss has the Premier League and Champions League football to focus on this season.
Conte has already landed Alvaro Morata, Tiemoue Bakayoko, Antonio Rudiger and Willy Caballero.
