An independent review of the tendering process, which was controversially put on hold early last month, was due to be presented to councillors at a finance meeting this week, but it has now been announced that Thursday's discussion has been postponed – despite city council chief executive Tom Aitchison confirming that he had received the report from Deloitte.
He said officials would not be in the position to share the findings with councillors by Thursday, and he admitted that he did not yet know when the report will come before a committee.
The delays have led to doubt about whether the whole tendering process will go through.
Some care groups claim that the initial winners of the 11 care contracts have agreed to put back the deadline for the formal signing of the contracts to 28 February.
During the period in between, the existing providers will continue to provide care.
Cllr Ian Murray, finance spokesman for the Labour group on the council, said: "We have not been told what happens next.
"The administration will be keen not to send it back to council because they don't have the numbers (of councillors to win a vote], but the next finance committee is not for another month."
Latest council figures show that more than 500 of the care clients involved in the process have now signed up to direct payments, which means they get money from the council to employ their own carers.
Cllr Murray said if all the direct payment requests go through, it is almost certain only a small number of the 11 care contracts would be able to go ahead as many would fall below client number limits.
The independent review was called amid concerns that there had not been a "complete separation between price and quality" in the initial tender process.
Ian Hood, co-ordinator of the Edinburgh-based Learning Disability Alliance Scotland, said: "The fact that the council has got the report in time for the committee but it is taking this length of time to analyse suggests it may have gone against the council.
"There is a lot of uncertainty at the moment and I have been trying to get an indication of what happens next. It is all up in limbo. Nobody knows what happens next and what the council will do about things like direct payments."