A group of 17 MPs aligned with the Australian Metal Workers Union on Tuesday threw their unanimous support behind the deputy premier, one of three candidates alongside Health Minister Amber-Jade Sanderson and Transport Minister Rita Saffioti.
Mr Cook is now thought to have a majority of left faction MPs in his camp despite the bulk of MPs tied to the United Workers Union having earlier backed in Ms Sanderson.
The right faction is expected to meet on Wednesday.
Emergency Services Minister Stephen Dawson said the metal workers union believed Mr Cook, who served as health minister during the peak of the COVID-19 pandemic and now holds the state development, jobs and trade portfolios, was best-placed to serve as premier.
He said Ms Saffioti, who is not aligned to a faction, would also have the union's support to serve as deputy to Mr Cook.
"Roger has been part of the leadership team now for a long time," Mr Dawson told reporters.
"Certainly one of our strengths as a government has been how we dealt with COVID-19. Roger, of course, was a big part of that.
"Amber's a fantastic minister. She's been a minister, though, for just over a year and a half.
"She's got a big task ahead in the current portfolio that she's got."
Mr Dawson played down talk of disunity within Labor's left faction and backed Ms Sanderson to one day lead the party.
"I'm confident that if Roger becomes the next premier of Western Australia, there won't be divisions," he said.
"We have been a very collegiate team for the last six years, we've not had much movement and I don't think that will change under Roger's leadership."
More than 25 Labor MPs are tied to the United Workers Union, with a majority backing Ms Sanderson at a meeting on Tuesday.
"I've been chosen with a clear majority to be the candidate to go forward for the leadership," she said after the meeting.
"I will now reach out to my colleagues across the caucus with a focus on unity and stability."
Ms Sanderson only became a cabinet minister in 2021, taking the environment and commerce portfolios, before stepping up to health during a meteoric political rise.
Ms Saffioti is yet to publicly comment on her intentions.
If the party is unable to settle on a candidate, it will likely have to canvass rank-and-file members in a process that could take weeks.
The entire parliamentary party is expected to meet early next week.
Mr Cook earlier made a public pitch for the job, saying he had the necessary energy, experience and support of his colleagues.
"As someone who's been acting premier on many occasions, I feel I know what is required to be premier," Mr Cook told Perth radio 6PR.
Like his senior colleagues, Mr Cook said he had only learned of Mr McGowan's shock decision to resign at a cabinet meeting on Monday shortly before it was announced.
Mr McGowan said the role of political leadership was relentless and the COVID-19 years had exhausted him.
"I just don't have the energy or drive that is required to continue in the role as premier or to fight that election, which would have been my eighth election as a member of parliament," he said, referring to the next state poll in 2025.
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