The Dutchman has been linked with a move to their Premier League rivals.
But the centre-back has suggested that if the team show signs that they are heading in the right direction, the Dutchman will see himself as part of their future.
"If we do well and we are going to progress and then hopefully do better than we do this year then I am very confident he will stay," he told the Star.
It is hardly surprising that the Merseyside outfit have reportedly pinpointed Koeman as one of the genuine candidates for the job as the work that he has done at St Mary's has been hugely impressive.
Though Nigel Adkins and then Mauricio Pochettino laid much of the groundwork at the south coast club, Koeman arrived as many of the team's best players were leaving. And yet, he managed to put a team together that not only embarrassed those who predicted that they would be going down, but qualified for the Europa League.
And with Koeman's men going into the final day of the season with a chance of booking a place in the continental competition once again, it would be no surprise if Everton viewed him as the man that could take them forward.
But van Dijk is confident that if Koeman believes that he can take Southampton forward, he will have no decision to make.