BetVictor now offer odds of just 10/3 on Van Dijk moving to Everton before September.
At the moment, there are no suggestions that the Toffees will make a move for the Southampton centre-back.
However, the shortening price offered on him moving to Everton is an intriguing development.
Van Dijk has recently signed a new contract with Southampton - suggesting he is happy at St. Mary’s.
Everton do have money to spend this summer, though, and Ronald Koeman is on the lookout for a new centre-back.
Koeman is known to be an admirer of Van Dijk, as he was the manager who brought the Dutch international to the south coast club.
Koeman is yet to bring a Southampton player with him to Everton, but there is no clause in his contract stopping him from raiding his former employers, as has previously been suggested.
Southampton have already sold key players Victor Wanyama, Graziano Pelle and Sadio Mane this summer.