Caterham's administrators will not fund the team to attend the first pre-season test if a buyer is not found in time.
Testing starts on 1 February at Jerez with the first race of the season taking place in Australia on 15 March.
"Talks with interested parties continue, but if a buyer is not found before the test, we will not put up the money to go," joint administrator Henry Shinners told BBC Sport.
"I wouldn't rule anything out but if we reach the first race in the same position, the chances of saving the team are virtually nil."
|Caterham in Formula 1|
|Debut: 2010 (as Lotus Racing)|
|Best race finish: 11th - Vitaly Petrov at the 2012 Brazilian Grand Prix|
Caterham missed the United States and Brazilian Grands Prix after entering administration.
However, a successful crowd-funding project saw them compete at the season finale in Abu Dhabi, where they failed to finish in the points with Will Stevens or Kamui Kobayashi.
In December, Shinners, of London firm Smith & Williamson, said they were in talks with three buyers.
Those same buyers remain interested, with talks planned for later this week, but a formal offer has yet to be made.
Shinners said there was a meeting of the team's creditors on 22 December where they voted in favour of the administrators' proposals, which broadly speaking were to continue to try to find a buyer for the team.
Caterham were able to get the team ready to compete in Abu Dhabi in just two weeks, but with many of their staff now in new jobs, that timeframe will likely increase for an attempt to compete in the first race of the season.
"We need to start moving in the next few weeks if a deal is going to get over the line," added Shinners.
If Caterham find a buyer and make it onto the 2015 grid, they will need to re-employ staff and sign two new drivers.