Vaughan Gething will be made first minister on Wednesday.
By Gareth Lewis and David Deans
BBC Wales
Welsh Labour politicians have held a meeting to discuss concerns about their newly elected leader, BBC Wales has learned.
Vaughan Gething was criticised for getting £200,000 from a firm owned by a man convicted of environmental crimes.
Members of the Senedd (MS) said they wanted Mr Gething to understand the level of disquiet in the party.
A meeting of 14 politicians was held on Monday evening, one source said.
Mr Gething is due to be confirmed as first minister in the Senedd on Wednesday after Mark Drakeford officially quits on Tuesday.
One MS told the BBC there was a “growing feeling in the Labour group that the donation should be returned, some even saying they won’t vote for him on Wednesday if he doesn’t”.
“I can’t see people following through on the threat. But with just 30 votes, unless the other parties abstain then all it takes is one Labour member to abstain to block it.”
Another said that no-one had said they would abstain in such a vote, which would only take place if it was triggered by an opposition party “but I don’t think people like feeling that it is assumed until he’s answered our questions”.
Normally, the opposition would have enough votes between the Conservatives, Plaid Cymru and Welsh Lib Dem leader Jane Dodds to force a tie, preventing a new first minister from being nominated.
But the suspension of Rhys ab Owen for six weeks means the government has a temporary majority of one with its 30 MSs.
A tied vote could still happen if a Labour member decided to abstain – but that is something that would cause a political crisis.
Mr Gething defeated Jeremy Miles in the Welsh Labour leadership contest, which ended on Saturday.
Earlier on Monday, he promised a review of campaign donations for Welsh Labour leadership contests.
At the weekend the Member of the Senedd for Cardiff South and Penarth refused calls to pay back the money from Dauson Environmental Group.
Dauson is owned by David John Neal, who was handed suspended sentences in 2013 and 2017, of three months and 18-weeks respectively.
Mr Gething defended his relationship with the organisation, denying he had lobbied for Neal’s subsidiary company Atlantic Recycling.
Image source, Welsh Government
Vaughan Gething, pictured with Rebecca Evans at Mark Drakeford’s final cabinet meeting, is expected to become first minister on Wednesday
Welsh Labour confirmed that any remaining unspent campaign funds would have to be given to the party.
Meanwhile, new figures suggest Mr Gething won over party members by a thinner margin in the leadership vote than he did members of trade unions and other groups
Climate Change Minister Julie James called for the review in the wake of the donations while former First Minister Carwyn Jones said the decision to take the money was “unfortunate”.
On Politics Wales on Sunday Mr Gething said: “Of course the donations have been a story and I recognise that. There’s always a point of learning and reflection.”
Asked by BBC Wales on Monday what he meant, he said: “Reflecting on what it means for future contests, to review where we are now and what that might mean in the future.
“Politics changes quite rapidly, from when Carwyn Jones was running to now, the world of politics is actually radically different.”
After his confirmation as first minister, attention will move to who Mr Gething will appoint in his cabinet and how many of those in his rival’s camp will get jobs.
Image source, Welsh Government
Mark Drakeford held his final cabinet meeting on Monday.
Mr Gething was due to have a “face to face conversation” with Jeremy Miles on Monday and said he had already been talking to people “on all sides of the contest”.
On Radio Wales’ Drive programme, Mr Gething’s campaign co-chairman Ken Skates said the money was needed to pay staff.
“He primarily needed it to make sure he had the best team behind him,” he said.
“It would have been possible, of course, to have expected people to volunteer their time.
“But if you’re going to stand up as a politician arguing that people should get a decent wage, you shouldn’t expect people to be working for nothing.”
Vaughan Gething says he cannot return a £200,000 donation
Meanwhile, a breakdown of the vote between party members and members of affiliated organisations including trade unions has emerged.
They suggest Mr Gething won the vote of party members by a thinner margin than he did affiliates.
The Welsh Labour leader won support from all the big unions, although his backing from Unite came under controversy after Mr Miles was invited to a hustings despite rules stipulating he could not be nominated.
First reported by WalesOnline’s Will Hayward and confirmed by a source speaking to the BBC, Mr Gething is understood to have won 50.7% of the membership vote compared to 49.3% for Mr Miles.
Of affiliates, Mr Gething won 52.7%, versus 47.3% for Mr Miles.
Precise figures for party members and affiliates are unavailable, although there are estimated to be about 18,000 members of Welsh Labour and 100,000 affiliates that could vote.
The party provided turnout figures of 57.8% for Labour and 9.4% for affiliates – which could roughly mean that about 10,000 members and 9,000 affiliates participated.
