Edinburgh's Labour group is awaiting a decision from party chiefs on whether to form another council coalition with the SNP.
Last week's election returned Labour as the second largest party in the capital with 13 seats, one more than in 2017, whilst the SNP came out on top retaining its 19 seats in the City Chambers.
Together, they are the only groups with enough councillors to form a two-party majority administration – which would be a more stable arrangement than the minority SNP/Labour coalition that's run the council over the past five years.
READ MORE: Edinburgh Election 2022: SNP remains largest party as Tory losses spark Lib Dem revival
However, a renewal of that deal has been cast into doubt in recent weeks, after Scottish Labour leader Anas Sarwar ruled out any 'formal coalitions' with the SNP or the Tories during the election campaign.
Sources said Labour's National Executive Committee (NEC) is set to issue guidance to Edinburgh group leader Cammy Day on whether to push ahead with another agreement or not.
It's understood other parties are awaiting the outcome of that decision before progressing talks on alternative options.
Following initial negotiations over the weekend, the Liberal Democrats, which doubled its seats on the council to 12 last week, ruled out entering any coalition with the SNP.
Group leader Cllr Robert Aldridge said discussions showed SNP councillors had "learned nothing from the difficulties of the last Council term and plan to simply continue with their previous approach", citing their "arrogance" and "inability to get basic council services right".
He added: "Liberal Democrats believe the people of Edinburgh deserve better than this. It is why our group has agreed we will not enter into any agreement with the SNP on Edinburgh Council.
“We remain open to continue our discussions with other parties. We want to work constructively in the interest of the city we serve and explore options on how the Council can change for the better."
Sources said officials have drafted a document comparing manifestos on key policy areas to assist parties in the negotiating process.
If no further agreement with Labour is reached it's expected the SNP will move to strike a deal with the Greens, which would produce a minority administration, possibly seeking support from other parties on an informal basis to get across the line.
Other possible outcomes are a three-way coalition between Greens/Labour/Lib Dems, producing a majority of 35 seats, and a Labour/Lib Dem/Conservative coalition with 34 seats.
Edinburgh SNP leader Adam McVey said discussions between his group and "progressive parties" are ongoing.
He said: “We emerged from Thursday’s election as clearly the largest party, having set out a positive, progressive vision for Edinburgh with a detailed programme to improve our local services.
"We will continue talks with progressive parties about how to take forward the change Edinburgh needs to be fairer, greener and deliver the best for our residents.”
Steve Burgess, Green Party co-convenor on Edinburgh Council, said: "Greens are very much open to working with other parties who share the priorities we were elected on, particularly on tackling the climate emergency and the cost of living crisis. Those are big challenges facing the city.
"The election results have thrown up a range of possible ways a council administration could be formed. There are two parties that could form an obvious administration because they have a majority of seats between them. They need to decide if they are going to take that forward.
"The newly elected Green councillor group have been meeting to discuss how best to push the new Council for the Greener and fairer Edinburgh that people voted for last week whatever happens. And we’ll be working with other parties about that whatever happens."
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