Bellamy laughed off the surreal subplot earlier on Wednesday, adding he had not spoken to Cooper since the former Swansea City, Nottingham Forest and Leicester City boss was appointed by Brondby in September 2025.
Brondby's communications director Soren Hanghoj rejected Barbarez's claim and said the player's omission was a "club decision", adding: "And there are not that many Wales fans in Brondby after all."
There will, though, be a sizeable contingent of Bosnian fans who make the trip to the Cardiff City Stadium with their side needing to beat Wales to remain on track to reach their first World Cup since 2014.
The winners in south Wales on Thursday are guaranteed a home final against the winners of Italy or Northern Ireland on Tuesday, 31 March.
Ranked 71st in the world, the Bosnians were edged out of automatic qualification by Austria when they conceded late in a final group game decider in Vienna.
"We cannot compare these two games, against Wales and Austria," said Barbarez.
"We took some conclusion from the Austria game and we have spoken about it for three days about the experience we have taken from it.
"We have a plan and every eventuality is covered, including penalties and extra time. We are optimistic. These are the games you play football for."
Forty-year-old former Manchester City striker Edin Dzeko is among the group of players who have travelled to Cardiff, though he is not guaranteed to start.
His Schalke team-mate Nikola Katic, formerly of Rangers and Plymouth Argyle, said: "The atmosphere in these kind of matches here is always brilliant and we will give our best.
"This is a serious team we are playing against, but we will play our own game and we are prepared for every eventuality.
"We have not had much success as a nation in the play-offs before, but that is not important for us; it is new for a lot of our players and our team is much stronger than previous sides."

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