Mr McGowan said an announcement on when the state's hard border would be eased would be made by the end of the month.
The state was supposed to reopen to the rest of the country on February 5, but was delayed due to large numbers of Omicron cases in eastern states.
"We are reviewing (restrictions) as we speak," he told reporters in Perth.
"The reality is though that we are getting the third dose vaccination rate up, the eastern states appear to be coming off their peak, which is a good thing."
One of the reasons Mr McGowan made to delay the border reopening was to allow more time to increase the booster dose rate in the state, which was lagging behind the rest of the country.
"By the time we reopen the interstate and international borders, we'll be one of the highest vaccinated places in the world with one of the safest populations in the world," Mr McGowan said.
It comes after the state reported 62 new cases of COVID-19 on Tuesday, as Western Australia deals with an outbreak of the virus.
Meanwhile, Health Minister Greg Hunt defended the government's handling of virus outbreaks in aged care facilities.
He said all aged care facilities had been visited by vaccination teams for booster shots, with 300 facilities having had second visits.
83.4 per cent of the eligible population in aged care have had their booster dose.
"In terms of workforce, over 82,000 surge positions have been made available, 50 million units of PPE have been provided to aged care homes," Mr Hunt told parliament on Tuesday.
Earlier this week, the national booster program passed 10 million doses.
The head of the country's vaccine rollout Lieutenant-General John Frewen said 17 million Australians were eligible for boosters.
"Another 144,000 people came through the doors yesterday. The uptake is really good, but we have a way to go still," Lt Gen Frewen told the Seven Network on Tuesday.
"It has never been more convenient to get a vaccine and there is good choice across the range of vaccines."
This week also marked the start of the rollout of the Novavax vaccine.
The vaccine is the fifth to be approved by Australia's medical regulator and the first protein-based vaccine to be used in the country.
Lt Gen Frewen said while the overall vaccination rate was more than 90 per cent, it was hoped more people would use Novavax to start their primary course of COVID-19 vaccinations.
"We have had more than 3000 GPs and pharmacies show an interest in stocking it and more than 2000 orders placed now," he said.
"We are now at 94 per cent of the nation who have come forward and had their doses. This is an extremely high number by any standard, and there is another six per cent of the nation potentially."
Tuesday saw a further 50 COVID-19 deaths reported, with 20 fatalities in Victoria, 16 in NSW, 10 in Queensland and four in SA.
There were 23,817 new infections, with both NSW and Victoria registering more than 8000 cases, Queensland getting 5286, 1138 in SA, 513 in Tasmania and 455 in the ACT.
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