Everton have wasted no time at all in the transfer window, having spent over £90million on five recruits already this summer.
And Ronald Koeman's side look set to turn their attention to Van Dijk.
The Toffees are about to pocket £75million from the sale of striker Romelu Lukaku to Manchester United in the coming days, which could fund a move for the Southampton defender.
And according to bookmakers Betfair, Everton's odds of signing Van Dijk have been slashed from 50/1 earlier this week to just 7/2.
Van Dijk has emerged as one of the most sought-after defenders in the Premier League this summer.
Everton's Merseyside rivals Liverpool looked set to sign the Holland international before they were forced to end their pursuit.
Southampton reported Liverpool for making an illegal approach for the Dutchman.
But Betfair reckon Liverpool are still the favourites to sign Van Dijk at odds of 11/8.
Southampton executive director Les Reed recently revealed that none of the club's top players are for sale this summer, including Van Dijk.
"None of those players are for sale," he told Sky Sports when asked about Van Dijk and right-back Cedric Soares.
"I can't make it any plainer than that and that's the way we mean to go forward.
"We built this squad over some time and think we have a strong squad. We will fine-tune it but, other than that, we are looking forward to a very competitive season and we plan to go forward on that basis.
"There may be players that go on the basis that it is the right thing for them and the club at that given time.
"But we don't expect that to be wholesale and this is simply doing sound business in the transfer window."
Source: Daily Express