UEFA announced on Tuesday the match was being moved to Kiev's Olimpiyskiy Stadium , which hosted the 2018 Champions League final between Real Madrid and Liverpool, because of security issues.
European football's governing body said its Emergency Panel made the decision "following the introduction of martial law into certain regions in Ukraine".
But on Wednesday, Vorskla aired concerns over the moving of the game, suggesting the Olimpiyskiy Stadium was not ready to host the match against the Premier League side.
Asked by local outlet Seven Sport if the game may not go ahead, president Roman Chernyak said: "It's a complete possibility. They made that decision without agreeing with anyone. At present there is uncertainty.
"The decision was made yesterday evening. It's hard for me to comment.
"Our goal is that our fans watch this game at our stadium. We have spent a lot of money on repairing our arena.
"We're all shocked. Nobody has asked us anything, no one has informed us. Moreover, the Olimpiyskiy Stadium is not ready for the organisational point of view.
"The fans got tickets to watch in Poltava - airplanes, trains and buses - as well as meeting at the stadium. What happens to these tickets? Or how to sell tickets to Olimpiyskiy for 70,000 people in a day?
"This is a decision taken without informing. The main question now is if the game will take place? Today, a pre-match training and press conference should be held. But where and how?"
Vorskla must beat Arsenal and hope Sporting CP do not beat Qarabag to stay in contention to qualify, with Chernyak determined to play Thursday's match at Vorskla's home stadium.
"At present, we are dealing with organisational issues," he added. "They gave us a stadium that is not able to host a home match of the Ukrainian team. That's why it is impossible for us to know anything at the capital's stadium.
"Because we have not applied to play at this arena from the very beginning. Who will be responsible for the security there? There are many open issues.
"At present, we are dealing with these. Why not play in Poltava?"