Two new locally acquired Covid-19 cases have been reported in Victoria, a day after Chief Health Officer Brett Sutton indicated the state was "on pace" to remove restrictions later this week.

According to Victorian health officials, both new cases are main close contacts of current individuals who had no population exposure throughout their infectious time.

On Sunday, when 13,764 vaccine doses were provided at state-run locations, the results were discovered among 16,932 test results reviewed.

Professor Sutton said on Sunday that the state was on track to ease restrictions this week, but he wanted more people to come in for testing because some Covid-19 instances may be going unnoticed.

Last week, an office and apartment building on Freshwater Place in Southbank was added as an exposure site for a variety of times between Thursday and Friday.

Authorities are still attempting to figure out how a number of mysterious cases are linked to the outbreak, but Professor Sutton said on Sunday that some of them have "early evidence of plausible linkages."

It's still unclear how the virus spread from a Wollert man afflicted with Covid-19 in South Australia to the City of Whittlesea outbreak and an Arcare Maidstone aged care worker.