The beleaguered Oxfordshire-based team has been plunged into crisis due to a bitter ownership row between founder Tony Fernandes and prospective buyers Engavest.
Caterham may not take to the grid in Austin and Interlagos in the next two rounds in order to give the team's administrators time to find a new buyer.
A statement from accountancy and investment management group Smith and Williamson revealed that the move, which also includes a deal to take over shareholding of the team, will provide a greater chance of finding a buyer.
Finbarr O'Connell, the administrator working on behalf of Smith and Williamson, has spoken to Ecclestone, who has agreed to allow Caterham to miss two races if necessary.
"In a telephone conversation today [Friday] between Finbarr O'Connell and Bernie Ecclestone, Mr Ecclestone agreed to support the administrators in their wish to sell the Formula 1 team to a party with the financial strength to sustain it into the future," read Smith and Williamson's statement.
"Mr Ecclestone also agreed to give dispensation to Caterham F1 such that it could if necessary miss the US and Brazilian Grands Prix but hoped that a new owner would be in a position to race the team at the Abu Dhabi Grand Prix."
The statement also revealed that several parties have voiced an interest in purchasing the team and hope to conclude a deal in the coming weeks.