Celtic lost 2-0 to Malmo in Sweden on Tuesday night, with the Scandinavians progressing into the group phase 4-3 on aggregate.
It is the second consecutive year that the Scottish champions have been knocked out in the last preliminary round after they were beaten by Slovenian outfit Maribor last season.
Defeat on this occasion leaves Celtic in danger of losing their prized asset Van Dijk, who has been linked with a move to Southampton for much of the summer.
Hoops boss Ronny Deila insisted after the game in Malmo that Van Dijk remains under contract and that there is no need to sell him, but the defender himself was unable to commit his future to the club after defeat to Malmo.
Asked if he would remain for Celtic’s Europa League campaign, the Dutchman told Sky Sports News HQ: “I don’t know, it is so close after the game.
“I can’t give my opinion on that right now. I’m very disappointed and it’s a terrible way if it ends like this. I don’t know what is going to happen.
“I’m not looking for anything. It’s a great place to be and they (Celtic) gave me a great opportunity to show myself so I’m very thankful for that.
“But if the opportunity comes and it’s the right opportunity for me then I’ll consider it, yeah, but that’s what every player, I think, would do.
“It’s still difficult. Celtic is an amazing club and I am very thankful for what they did for me. We’ll see what is going to happen.”
Van Dijk doesn’t know if Southampton have already made a move, adding: “I think you need to ask the board that. I don’t know what is going to happen in the upcoming days but we’ll see.”