It was anticipated that the FIA would reveal on Wednesday those that failed to comply with last season's £114million budget cap.
Red Bull faced unproven allegations at last weekend's Singapore Grand Prix that they exceeded F1's cost cap last term - bringing into the spotlight the legitimacy of Max Verstappen's already controversial championship win over Lewis Hamilton.
But in a statement, the FIA said the "analysis of financial submissions is a long and complex process that is ongoing", with news now not expected until after this weekend's Japanese Grand Prix, a race where Verstappen, 25, could secure his second title in as many seasons.
A statement from the sporting federation read: "The FIA informs that the conclusion of the analysis of the 2021 financial submissions of the Formula One teams and the subsequent release of Certificates of Compliance to the Financial Regulations will not take place on Wednesday, 5 October.
"The analysis of financial submissions is a long and complex process that is ongoing and will be concluded to enable the release of the Certificates on Monday, 10 October.
"The Financial Regulations were agreed unanimously by all competitors, who have worked positively and collaboratively with the FIA Cost Cap Administration throughout this first year under the Financial Regulations.
"As previously communicated, there has been significant and unsubstantiated speculation and conjecture in relation to this matter, and the FIA reiterates that until it is finalised, no further information will be provided.
"The FIA also reiterates that any suggestion that FIA personnel have disclosed sensitive information is equally baseless."
Red Bull have been accused of spending more than they were allowed, possibly by over five per cent, which would equate to more than USD7.25m (£5.6m).
Sanctions available to the FIA for a breach range from a reprimand, to financial penalties, to the deduction of drivers' and/or constructors' points - and even exclusion from the championship.
Hamilton was denied a record eighth crown when he was beaten by Verstappen at a deeply contentious winner-takes-all finale in Abu Dhabi on December 12. Verstappen took the title by eight points.
The Dutch driver is also the runaway leader of this season's title battle, and will be crowned champion in Suzuka on Sunday if he wins and sets the fastest lap.
Mercedes boss Toto Wolff demanded the FIA take robust action against any team that has broken the rules. Christian Horner said he is confident Red Bull are not in breach and accused Wolff of "hugely defamatory, fictitious claims".
The Red Bull team principal also threatened legal proceedings against Mercedes during a toxic weekend in Singapore.
Asked in the aftermath of last Sunday's race in Singapore - which was won by Red Bull driver Sergio Perez - if he was nervous about the FIA's verdict, Horner said: "No. We're absolutely confident in our submission.
"Our audit was signed off by our auditors. We believe we are comfortably within the cap."