Organisers say the chances of the Rugby League World Cup going ahead this year are "50-50" with a final decision expected in the coming days.
Australia and New Zealand pulled out of the event, citing "player welfare and safety concerns" related to Covid-19.
Jon Dutton, chief executive of the tournament in England, says their withdrawal is "irreversible".
"I think it's 50-50 [that it goes ahead], but we won't know until we listen to the players," he said.
"We have signed a memorandum of understanding with the Rugby League Players' Association and I cannot speak highly enough of Clint Newton and his team, who have been very supportive.
"I think a lot of the concerns are more about wellbeing rather than safety. Without the players, we don't have a tournament and that's why we need to listen to them."
Following an emergency meeting of the event's board on Wednesday, Dutton said it will explore what appetite there is to go ahead as planned with the contest,which is scheduled to start on 23 October.
Dutton told BBC Sport "time is no longer on our side" and a final decision about the staging of the tournament, which includes men's, women's and wheelchair competitions, will come "in days, not weeks".
In a statement, Dutton also said the board "recognise the need to bring clarity and certainty to the situation", adding it has been in regular contact with the UK government, saying its support has been "invaluable".
"The board have instructed myself and the RLWC2021 team to continue to hold further urgent discussions with all stakeholders, particularly the players, aimed at correcting misinformation as well as measuring the sentiment on proceeding with the tournament," Dutton added in the statement.
"While the board reiterated the determination to deliver the biggest and best-ever Rugby League World Cup in history, they are also realistic about the significant challenges that threaten that ambition."
Melbourne Storm and Queensland prop forward Christian Welch, who is also a director of the Rugby League Players' Association, says players were not consulted before reigning champions Australia, the 11-time winners, and New Zealand, who lifted the trophy in 2008, withdrew last week.
Dutton said it is "fundamental that players have a voice and a choice" in what happens with the event.
"We want to get out and supply the players directly with the information," he said.
"We want to sit down, we want to talk to them on a face to face basis and understand their concerns and then take a view in the coming days whether it is still achievable.
"This is a seminal moment for international rugby league and the work we have invested and position we have gotten the tournament into."
Talks with players include informing them of the "extraordinary measures" being undertaken to protect their wellbeing, while competing nations are being briefed so they can "fully understand any new or developing issues that will prevent them travelling to England in October".
Organisers also confirmed they are in talks with the game's global governing body, International Rugby League, about replacement teams and "the implications" of Australia and New Zealand's absence.
Dutton said the inclusion of an Indigenous Australian side and New Zealand Maori team are options "absolutely" being considered.
"It is a very inclusive and diverse tournament," he said. "Certainly some reports on the indigenous and Maori teams are of interest to us.
"At the end of the day, the decision on those teams would be for International Rugby League, and we are working closely with Troy Grant, the chairman, and his team."
- The life and legacy of one of the UK's greatest talents: Join us for a celebration of Amy Winehouse
- Smalltown Boy: A powerful tale of a young gay man told through a disco classic