The Tories are expected to take control of Northampton Borough Council.
Conservative Phil Jarratt is being tipped as the likely leader of the authority after Labour lost 15 seats in last week's local elections.
However, the Liberal Democrats are believed to be angry that Labour appear not to be ready to oppose the Tories' move for power.
A spokesman for the council said: "It is anticipated that the Conservative group will announce their intention to form the administration, with Councillor Phil Larratt as Leader of the council."
After the election on 1 May, the Conservatives had the largest number of seats but no overall control.
The council now comprises 19 Conservatives, 17 Liberal Democrats, and 11 Labour members.
The council's annual meeting takes place on 22 May.