Promising striker Barry rejected a three-year contract at The Hawthorns to join the Catalan side in July 2019.
Under set FIFA compensation rules for youngsters who move abroad, the La Liga side owe the Baggies £235,000 for the England youth international.
Barry, 17, has since left Barcelona to join Villa for a fee of around 1million euros or £880,000. But the Spanish side have still not paid Albion the money they are entitled to for a player they developed from the age of seven.
Earlier this week, finance experts Deloitte revealed Barcelona hit a record revenue of $959.3million in the 2018/2019 season
That figure made them the biggest cash-generating football club in the world for the first time.
Statistics also showed Barcelona, Real Madrid, and Juventus are the only three European football clubs with the average annual player salary above $10 million.
Despite those riches, Barca have refused multiple requests from Albion for the payment they are due for Barry.
The Baggies have taken their case to world governing body FIFA having grown increasingly frustrated with the situation.
But they believe Barcelona think they will go away and stop asking the longer they withhold payment – with the fee for Barry fairly minimal in football terms.
Albion, though, are adamant that will keeping fighting and are determined to keep working with FIFA – or even take their case to court – if that is what it takes.