Under Tennis Victoria's advisement, the tournament is able to progress as it is run by an independent body.
"For all competitions operated by Clubs, Associations or Venue Operators, the decision to postpone or cancel is at the discretion of the relevant Club, Association or operator," Tennis Victoria's statement on Monday said.
"Tennis Victoria Staff will be on hand to support your decision making. Please contact your relevant Tennis Victoria staff member team if you need further support."
Despite the decision, ELTC said they would give refunds to anyone who requested one.
"At this stage, the tournament will continue to play all events as normal," the club said in a Facebook post on Tuesday afternoon.
"The directions from Tennis Vic allows our tournament to still go ahead although anyone with concerns can send an email to withdraw from the tournament and receive a full refund.
"Please be advised that with the constant changes surrounding COVID-19, the ELTC committee are having a meeting on Thursday evening to discuss this matter further.
"We will continue to keep you updated and thank you for your patience."