Thomas Cook, one of the world's oldest and largest travel companies, is holding talks with shareholders in a last-ditch bid to avoid going bankrupt.
A collapse could leave around 150,000 travellers from Britain stranded, along with tens of thousands of travellers from other countries.
The British government may have to lease planes to get its citizens home.Sunday's meeting, first reported by Sky News, is taking place at the London-based law firm Slaughter & May.
Officials from Thomas Cook were not available for comment.
Thomas Cook confirmed on Friday it was seeking 200 million pounds ($398 million) in extra funding to avoid a collapse.
It said it was in talks with stakeholders such as the Chinese shareholder Fosun.
Unions have urged the British government to intervene financially to save jobs if the company cannot raise the necessary funds.
Foreign Secretary Dominic Raab told the BBC's Andrew Marr Show that contingency planning was underway across Government departments.
"I can reassure people that in the worst-case scenario, the contingency planning is there to avoid people being stranded," he said.
Meanwhile, the Daily Mail reported that British holidaymakers were being "held hostage" in a Tunisian hotel over fears Thomas Cook will go bust.
Security guards at the Les Orangers beach resort near Tunis were keeping the gates shut while hotel staff demanded money over fears they would not be paid, guests said.
Many tourists are refusing to cough up as they have already paid Thomas Cook for the holiday, leading to a stand-off.
"We can't leave the hotel. I'd describe it as exactly the same as being held hostage," said Ryan Farmer from Leicestershire.
Another customer, Dean Williams, said the hotel had "taken it upon themselves to charge the customers as they haven't been paid by Thomas Cook".
Williams said the hotel had switched the WiFi off and a coach had arrived at 8.20pm to take guests to the airport but the hotel would not permit them to collect passengers.
The British Consulate in Tunisia has reportedly been made aware of the situation at the hotel.
- AP, Daily Mail