Mengele came to be known as the "Angel of Death" for the horrific experiments he performed on prisoners at the Auschwitz concentration camp and for his role selecting who would die in the gas chambers.
Ms Logan told Fox News host Pete Hegseth that "people" had told her that when they see Dr Fauci, the Director of the National Institute of Allergy and Infectious Disease, they see Mengele.
“What you see on Dr Fauci – this is what people say to me: that he doesn’t represent science to them. He represents Joseph Mengele. Dr Josef Mengele, the Nazi doctor who did experiments on Jews during the second World War and in the concentration camps,” she said.
Ms Logan made the comments on 29 November, and has faced repercussions for them ever since.
Prior to the comments, Ms Logan hosted a show on Fox News' digital streaming platform Fox Nation and also appeared regularly as a guest on the television network. However, after she compared Dr Fauci to a murderous Nazi, Fox News has not booked her on any of its shows.
WhenThe Daily Beast asked her what her standing was at Fox News, she said "I don't really know."
"I'm not on their payroll. So I, you know, I'm not in communication with them," she said.
On Monday, talent agency UTA chief communications officer Seth Oster confirmed to Mediaite that they dropped Ms Logan several weeks ago, meaning she has lost her television gigs and her representation since comparing Dr Fauci to Mengele.
A company insider told Mediaite that Ms Logan was let go as a direct result of her "unacceptable" comments made toward Dr Fauci.
Dr Fauci appeared on MSNBC, where host Chris Hayes asked him about Ms Logan's comments.
The doctor acknowledged that he was aware of Ms Logan's remarks, and claimed that Fox News did nothing to discipline her.
"She's completely incorrect in everything she says. What I find striking [is] how she gets no discipline whatsoever from the Fox network, how they can let her say that with no comment & no disciplinary action. I'm astounded by that," Dr Fauci said.
He went on to called her comment an "insult to everyone who suffered and died at the hands of the Nazi regime in the concentration camps."
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies