It comes after Ferrari team principal Mattia Binotto warned they may not be able to continue if budget caps are further slashed following the global pandemic.
Teams agreed on a budget cap of $277 million ($145m US) for 2021 but the economic impact of coronavirus could see further cuts.
“The 145m US dollars level is already a new and demanding request compared to what was set out last June,” Binotto told The Guardian .
“It cannot be attained without further significant sacrifices, especially in terms of our human resources. If it was to get even lower, we would not want to be put in a position of having to look at other further options for deploying our racing DNA.
“F1 has to be the pinnacle of motorsport in terms of technology and performance. It must be attractive for the car manufacturers and the sponsors who want to be linked to this most prestigious category.
“If we restrict costs excessively then we run the risk of reducing the level considerably, bringing it ever closer to the lower formulae.”
Binotto’s admission places further doubts over the future of Ricciardo, who is currently off-contract after this season at Renault.
The Australian star admitted earlier in the week that he would not rule out a return to Red Bull, where he had seven Grand Prix victories.
Sebastian Vettel has reportedly been given two weeks to finalise a deal with Ferrari and if he does not, Ricciardo was floated as an alternative.
But that now may be in doubt with Binotto’s frank warning about the team’s future in the Formula One amid the coronavirus chaos.
Ricciardo joins Vettel, Lewis Hamilton and Valtteri Bottas as big-name stars who are off-contract at the end of the year but with no races so far in 2020, they have little to base their decisions off.