Guilfoyle, 48, is a former San Francisco and Los Angeles prosecutor who was married for four years to California Lieutenant Governor Gavin Newsom, a strident critic of Mr Trump and his policies, particularly on immigration.
"I've never been someone who's motivated by financial interests", she said.
Guilfoyle claims that she has that kind of relationship with the president, having known him and his family for over a decade since they met at a charity event in NY.
"The president is in ... a unique position to communicate daily and directly with the country without using the press as his messenger", he continued, citing President Donald Trump's millions of Twitter, Facebook, and Instagram followers.
Following the firing of FBI Director James Comey, current press secretary Spicer was notoriously absent for a number of days from White House press briefings. Trump is known to watch Spicer's briefings closely and critique his performance, and observers have commented on Sanders' performance favorably in comparison to Spicer.
A senior White House aide also told the Daily Mail on Wednesday that the idea of Guilfoyle in the White House press room is "a total non-starter". Her name was mentioned during the initial interviews for Press Secretary job, a position that eventually went to Spicer.
"Just don't have them", Trump said to Fox News host Jeanine Pirro.
Guilfoyle has served as a cohost on The Five on Fox News Channel since 2011.
According to several White House officials, President Trump is considering reducing the press secretary's public appearances after months of turbulent press briefings. "Even if they wanted to cease the White House briefing, which would get a lot of people upset, I think he should be doing more of these press conferences himself".
"As long as they're having fun, they're getting exercise, they're enjoying themselves, and you know, that's what this is all about". I think it'd be a fascinating job. It seems to me that you're playing a very unsafe game with the currency of the credibility of the President of the United States.