The West Australian capital and neighbouring Peel region were due to emerge from three days of lockdown at midnight Monday, but Mr McGowan has tempered expectations, and is due to provide an update through the day.
"I'm sure there will be some further measures that continue," he told reporters on Sunday.
"What they are, we won't know until tomorrow morning. We'll get health advice ... and I think people should get used to the prospect that there will be some further measures continue beyond Monday."
The premier was expecting there to have been more than Saturday's 12,000 COVID tests completed on Sunday, which would help health officials determine the path forward.
"If there's further cases what we do will be more than perhaps there is now. It all depends on the circumstances. I can't predict what will happen. There will be an extension of some form of controls."
On Sunday the state recorded two new coronavirus cases among returned overseas travellers in hotel quarantine. There were no further community-transmission diagnoses.
The lockdown was sparked by two 'local' transmission cases which have been traced back to a Perth Mercure Hotel used for quarantine.
Late on Sunday authorities continued to search for and test hundreds of close and casual contacts of the confirmed cases.
A man aged in his 40s tested positive on Saturday after dining at a restaurant along with two other confirmed cases. His household contacts have been cleared of the virus, but authorities have extended the list of possible transmission sites, including a childcare centre, based on his recent activities.
Mr McGowan remains locked in a verbal battle with the federal government over management of the states' quarantine schemes.
He wants Canberra to open air bases and Christmas Island to accommodate the travellers, adding that it's the Commonwealth's constitutional responsibility to handle the quarantine scheme.
Defence Minister Peter Dutton says the facilities are not fit for purpose and that states had previously agreed to the quarantine scheme.