Celtic take on Ajax for the first time since 2013 on Thursday in the Europa League.
Celtic last faced Ajax in 2013, when both teams were drawn in the same Champions League group. In that season, both teams beat each other in front of their own fans, with Celtic winning 2-1 at Parkhead, but losing 1-0 at the Amsterdam ArenA.
As the Bhoys prepare to head to Holland again, Van Dijk has warned that they are in a better place now than they were two years ago - and he has suggested that Ajax will be in for a tough test when they meet Ronny Deila's men.
"It will be an interesting duel, as both teams did not seem in great form," Van Dijk said. "Ajax will have to make the game, as Celtic will lie in wait for an opportunity.
"They know exactly where Ajax are vulnerable and they will be happy in Scotland with a draw in Amsterdam.
"At home Celtic could win. The fanatical supporters bring something extra. I think that Celtic have improved since 2013, when we met Ajax in the Champions League. They have become stronger and there is more competition for places."
Despite the improvements that Van Dijk speaks of, Celtic's progress wasn't rapid enough to convince the 24-year-old to stay at the club.
Their failure to qualify for the Champions League group stage for the second season in a row was a bitter blow, and Van Dijk moved to Premier League outfit Southampton as a result.
So far the powerful defender has made one appearance for the Saints, helping them to keep a clean-sheet against West Bromwich Albion on his debut.
Celtic, meanwhile, have worked hard to replace Van Dijk, bringing in the likes of Dedryck Boyata and Jozo Simunovic in an effort to fill the void that he is left in their squad.