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A Football League spokesman told the site that the issue is "under review" but no decision is likely before Swansea and Carlisle meet at Cardiff's Millennium Stadium.
The competition will now be known as the Football League Trophy.
Swansea chairman Huw Jenkins told BBC Wales Sport they have not received any money for progressing through the competition.
He expects to lose out on an estimated £75,000 if they win on Sunday.
"Unless a last-minute sponsor comes in for the actual game on the day, we have to accept we're going to struggle to get any prize money from it," said Jenkins.
"The players are on bouses to get through to the final, and those bonuses are based on prize money so this does hit our earning power on the day.
"But we have a commitment to honour the bonus contracts so obviously we'll do that."
Despite the loss of a sponsor, both clubs are still set for a bumper pay-day on Sunday because they will receive 45% of the total gate receipts.
Swansea have already sold 22,000 tickets and Carlisle expect to break the 13,000 barrier this week.