Vale of Glamorgan council leader John Thomas is set to be ousted as head of the authority by fellow Conservatives.
Local party members are backing Vincent Bailey to take over following their annual general meeting last night.
For such a change, Councillor Thomas would have to lose a council vote of no confidence or voluntarily step down.
The row over the future of Llancarfan Primary School is understood.
Several councillors had joined parents in opposition to a decision to relocate pupils to a new school to be built in Rhoose, which they claimed amounted to a closure of Llancarfan.
Gordon Kemp was the only cabinet member to object to the plan, and he was later sacked when he joined ten other Conservative councillors in refusing to back last month's council budget.
The LDRS is also aware of "serious discontent" with Councillor Thomas among Tory backbenchers over a series of PR blunders, including proposals for new parking charges throughout the Vale of Glamorgan.
Councillor Thomas has been leader since the May 2017 election, when the Conservatives gained control of the authority from Labour.
Vincent Bailey, who chairs the council's environment and regeneration scrutiny committee, was one one of the newly elected Tory councillors that year, beating Labour to win the Dyfan ward in Barry.
He was previously an aide to former Welsh Conservative leader Andrew RT Davies, who won election to the council in February vowing to fight the Llancarfan proposals.