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Victorian Premier Daniel Andrews is expected to announce the border closure at a press conference at 10.45am on Monday.
It has been reported Mr Andrews, NSW Premier Gladys Berejiklian and Prime Minister Scott Morrison held crisis talks overnight.
The border between the two states has remained open throughout the health crisis, as towns share infrastructure, including the Albury-Wodonga Health public hospital.
"I'm not interested in closing our borders I don't think that makes a lot of sense for us," Mr Andrews said in March.
Twelve Victorian postcodes and nine public housing towers have been put into lockdown in order to prevent the spread of the virus in the state, which now has 2536 confirmed cases. More than 550 remain active.