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Mr Shorten has long maintained he was unaware of any investigation until Buzzfeed made inquiries about the story in July.
Prime Minister Malcolm Turnbull said this week that Mr Shorten's claim that "this has all come as a surprise to him is simply not credible".
Opposition Leader Bill Shorten and Labor frontbencher Tony Burke.
Photo: Alex EllinghausenIn March, Mr Turnbull said he was unaware that his then deputy Barnaby Joyce was having a baby with his staff member Vikki Campion despite a key adviser in the PM's office signing a job transfer for Ms Campion.
Ms Husar has strongly denied the allegations in the Whelan investigation and accused former staff of running a campaign to "ruin my reputation".
The allegations include sexual harassment of staff, using taxpayer funds for a nanny for her three children and diverting party fundraising into a personal bank account.
The western Sydney MP and Labor frontbencher Jason Clare have also both vehemently denied further allegations that she exposed herself to him while in his office.
Asked on the ABC Insiders program if she would be disendorsed from the Labor Party if the findings were damning, Mr Burke said the party "would deal with the report when we have a report".
Ms Husar holds the seat of Lindsay by a margin of 1.1 per cent. The electorate, won from Liberal MP Fiona Scott in 2016, is seen as crucial to Mr Shorten's chances of winning the next election.
Labor-left Penrith mayor Karen McKeown is among those being touted as a possible replacement for Ms Husar should she be disendorsed and move to the crossbench or resign ahead of the next election.
NSW Labor has asked its members to refrain from commenting on the ongoing investigation.
"It is a cause of some delay to the process and is serving to escalate tensions in an environment where parties to the assessment have expressed concerns about the impact of this matter on their wellbeing," it said in a statement.
“The independent assessment is reaching its final stages and NSW Labor expects to be briefed by Mr Whelan in the coming weeks. NSW Labor will not be commenting on any matters which may be before the independent assessment.”