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Sources said the Capital's Labour group leader Cammy Day had been in talks with Scottish party headquarters about the possibility of renewing the SNP-Labour coalition, but it was made clear such a move would be vetoed.
Scottish Labour leader Anas Sarwar said ahead of last week's elections he did not want formal council coalitions between Labour and other parties, especially the Tories or SNP. But it is understood Councillor Day was keen to see if there could be some flexibility. However, a source said: “The message he got back was No.”
The SNP won 19 seats at the election, Labour 13, the Lib Dems 12, Greens 10 and Tories nine.
An SNP-Green coalition has been seen as an obvious option from the start, especially in view of the SNP-Green partnership in the Scottish Government. But conversations have taken place over the past few days between various different parties, both in online meetings and face-to-face at the City Chambers.
Other potential combinations which have been floated include a Labour, Lib Dem, Green coalition, which would add up to a majority or a Labour-Lib Dem minority coalition, but it has not been clear whether such arrangements would also fall foul of Labour’s coalition ban.
However, one council insider said: "It seems Labour is not going to be allowed to do any kind of deal at all, which opens the door for the SNP and Greens to announce they will come together to form a minority administration."
Both the Greens and SNP group leader Adam McVey were said to be concerned that without a majority, a coalition between the two parties could be outvoted any time the other parties chose to combine.
But the insider said an SNP-Green coalition was now almost the only viable option and played down the likelihood of Labour, Lib Dem and Tory councillors regularly finding common ground. "You would need all three opposition parties, which are quite different, voting together to defeat the administration – that may happen from time to time, but it would be the exception rather than the norm.”
However, if an SNP-Green coalition is formed, the opposition parties could seek to install one of their own councillors to be Lord Provost in a signal that they did not want to be ignored.
Lib Dem group leader Robert Aldridge, who is the longest-serving member of the council with nearly 40 years at the Chambers, could be nominated for the post at the first meeting of the new council, scheduled for May 19.
One source said: “Councillor Aldridge is widely respected across the parties. If he were to be proposed for Lord Provost it would be putting down an early marker that the new administration was not going to get its own way all the time, it was going to have to reach out.”