The French club made history last August by becoming the first overseas team to win the trophy, but their 20-14 victory over Warrington Wolves at Wembley was witnessed by a crowd of just 50,672, the lowest since the Second World War.
That had a significant impact on the finances of the Rugby Football League [RFL], whose projected income from the event was down by around £800,000.
Both Catalans and Canadian club Toronto Wolfpack - now coached by former Leeds Rhinos boss Brian McDermott - had previously competed as guests in the Challenge Cup, but were asked, late last year, to lodge a bond of £500,000.
Toronto refused to pay up and will not feature in this year’s competition and now Catalans have urged the RFL to reconsider, with chairman Bernard Guasch saying it would be “irresponsible” for his club to pay the bond.
Fellow French club Toulouse Olympique did not enter the Challenge Cup in 2018 and will be absent again this year.
In a club statement, Guasch said: “The club has been officially advised in December that a £500,000 deposit will be asked by the RFL to play in the Challenge Cup in 2019.
“We, as a club, want to participate in this prestigious competition and defend our title, but it would be irresponsible to accept this decision.
“Thus, we have asked the RFL to reconsider its demand and we are now waiting for a decision.
“The players would be very frustrated not to be able to defend their title and we hope that we’ll have an answer as soon as possible.”
There is now a possibility Catalans could be excluded if they fail to hand over the bond.
Neither Catalans nor Toronto are full members of the RFL and have no automatic right to enter the Challenge Cup, but it will be a major embarrassment for the governing body if the holders are not in the draw for the sixth round.
Catalans’ Wembley victory created huge positive publicity for the sport with Dragons players parading the cup before a Barcelona FC game at the Nou Camp last autumn.
They are due to play Wigan Warriors there in a Betfred Super League clash in May.
In a statement, the RFL said: “We have been surprised and disappointed by the uncertainty over the Catalans Dragons participation in the 2019 Challenge Cup, which surfaced just before Christmas.
“We have been in discussions with the club since then and will continue those discussions to search for a solution.”
The RFL, which reported a loss of £2 million in its last set of accounts for 2017, is still searching for a Challenge Cup sponsor after Ladbrokes failed to renew its backing.