Wales' First Minister Vaughan Gething looks set to face a vote of no confidence when the Senedd returns next week.
The Welsh Conservatives are said to be very likely to table one ahead of a deadline of 18:00 BST on Wednesday, with the vote to take place on 5 June.
Mr Gething has faced unrelenting pressure after accepting £200,000 of donations to his recent Welsh Labour leadership campaign from a company whose owner was convicted of environmental offences.
Labour holds 30 of the 60 seats in the Senedd, so for the vote of no confidence to succeed at least one Labour Member of the Senedd would need either to vote in favour of the motion or abstain.
On 17 May the Senedd Conservative leader Andrew RT Davies said it was "odds-on" that a no confidence motion would be called.
He was speaking after Mr Gething sacked one of his ministers, Hannah Blythyn, for leaking messages to the media, something she denies.