"But we have to be alive to new evidence and obviously what has occurred here."
He said the new variant had been identified in two positive cases in the West Melbourne cluster and it was "suspected" it had first spread between two grade five students.
Professor Sutton said health authorities believed the first grade five student infected was in school for "two or three days" while infectious.
Those two cases were part of a family, made up of two adults and two children, who travelled to NSW's Jervis Bay.
Professor Sutton believed one of the parents of that family was "likely to be the index case" of the West Melbourne cluster of seven, and health authorities were rushing to find where they first contracted Covid-19.
"The Delta variant is the one that has become the predominant variant in India," Professor Sutton said.
"It has obviously had very high transmission potential, because it spread extremely rapidly across India to become the predominant variant, almost the exclusive variant there, and in surrounding countries, Nepal, Bangladesh, Sri Lanka are also affected by a significant uptick in cases related to that variant."
The two cases identified as the Delta variant were two of four new local infections recorded in Victoria on Friday.
The active number of cases linked to clusters across Melbourne has grown to 64.