"Somewhere above 80 per cent we'll try and set the date," he told The Western Australian on Wednesday.
"I don't know whether it'll be February, March or April, I suspect it will be one of those months."
Western Australia, along with Queensland are lagging behind the rest of the country with the vaccine rollout.
Only 35.7 per cent of Western Australians aged 16 and over are fully vaccinated and 54.8 per cent have had at least one dose, according to Australian Government's Health data.
So far, 35.8 per cent of eligible Queensland residents have been fully vaccinated, and 54.3 per cent have received at least one dose of the vaccine.
Meanwhile, in COVID-ridden New South Wales, 42.7 per cent of residents over 16 are fully vaccinated, and more than three quarters (75.6 per cent) have had at least one jab.
WA playing 'catch-up' with vaccine rollout
The Premier has called for more COVID-19 vaccines supplies in WA, taking a not-so-subtle swipe at NSW, who have been given priority access as the state continued to see more than 1,000 COVID-19 cases a day.
Mr McGowan said, while he had supported NSW receiving extra vaccine supplies, he feels WA is being "punished" for doing the right thing.
"The states which provided that additional support to New South Wales now need to be given out catch-up supplies, in particular of Pfizer," he told reporters on Tuesday.
"We can't have a situation where some states are punished for doing the right thing for New South Wales.
"You can't have a situation where you're penalised when you give your doses to New South Wales and you don't get a proper full catch-up."
Mr McGowan said Western Australia has "done our bit" to assist NSW and now it's time to get their share.
"We have provided, in the course of the last couple of months, 260,000 in N95 masks to New South Wales. We have medical teams in western New South Wales working on the outbreak there to vaccinate," he said.
"All our contact traces, 50 or so, work every day contact tracing for New South Wales and we kept all of our industries open, providing all the income the Commonwealth Government pours into New South Wales.
"We’ve done our bit, we’d like our share of Pfizer and now in Western Australia. We want to have a boost in our supply of Pfizer to make up for what we provided to New South Wales willingly.
"It’s incumbent now on the Commonwealth Government to make sure they provide that boost back to States like Western Australia and South Australia and Queensland."