It is likely to be made up of Liberal Democrats – who secured the most seats – Labour and others.
Potential council leader and Liberal Democrat group leader Councillor James Gibson-Watt confirmed that discussions with potential coalition partners are taking place – but would not be drawn on potential outcomes.
He said: “Negotiations are under way and I’m confident that we’ll be able to form an administration in good time for the AGM.
“I’d rather keep it confidential for the moment, but I do think we’ll be able to put together a very good administration.”
Councillor Gibson-Watt did confirm that the Conservative group would not be part of the administration as they are “too far apart on too many things”.
He added: "It wouldn’t work on either side."
A Lib Dem group meeting was held on Monday night to discuss the situation.
Labour group leader Councillor Matthew Dorrance said: “I have spoken to James; discussions are ongoing and there’s more work to do – we plan to talk again.
“It is hoped we will have a functioning administration by the annual meeting.”
With Labour likely to bring nine councillors to the coalition the figures go up to 33 of 68 councillors – short of an outright majority of 35.
To reach a majority it is expected that the Lib Dems will ask the Green Party’s new councillor, Jeremy Thorp to join the group.
Further additions will depend on what happens to the bloc of 17 independent councillors who were voted on to the council.
It is expected that the 17 will fragment into smaller groups – one of which could join the coalition.
Powys Conservative group leader Councillor Aled Davies said: “I’m not expecting to be part of the cabinet in the near future.
“I have congratulated James (Gibson-Watt) and I am a bit worried with what the Liberal Democrats promised on the campaign trail and that it will be impossible to realise, and I want to make sure schools will get the investment they need.
“We did reasonably well in Montgomeryshire, we returned the same numbers that we had in 2017 and were one vote away from gaining another ward.
“The performance in Brecon and Radnorshire was disappointing with only one member being elected, but the Independent group received the biggest hit.”
“We want to be a constructive opposition and will be working to make sure the people of Powys receive improving and the best services possible.”
The annual meeting is pencilled into the council calendar for Thursday, May 26.