Guilfoyle now co-hosts "The Five" on Fox News and was supposedly a top candidate for the job after Donald Trump's election but lost out to Spicer.
"The challenge they have is that the president sometimes moves so rapidly that they don't get a team around that gets it organized", said Newt Gingrich, the former House speaker and Trump ally.
Pressed by Pirro on whether he asked Comey for his loyalty, Trump responded: "No, I didn't, but I don't think it would be a bad question to ask". "It's a challenging job, and you need someone really determined and focused, a great communicator in there with deep knowledge to be able to handle that position". The president himself raised the prospect last week of secret recordings he's made of White House conversations, and Press Secretary Sean Spicer didn't contradict him, refusing to confirm or deny the existence of such recordings. And then, with a bit more obvious shade, "Very tough position he's in - I wish him the best, and I know he puts a lot of effort into it".
A dozen White House officials and others close to Mr Trump detailed the president's decision-making and his mood on the condition of anonymity in order to discuss private conversations and deliberations.
She was originally considered for press secretary during the presidential transition, but the job went to Spicer, who was spokesman for the Republican National Committee.
Guilfoyle is even talking about Spicer as if he is already gone: "Sean Spicer is a very nice man and a patriot".
National Police Week honors law enforcement across the country
The names of 394 officers that were killed in the line of duty were read out loud, 143 of those officers have died past year . The White House will be illuminated with blue lights tonight to honor law enforcement, President Trump announced Monday .
If Guilfoyle takes the job, she would leave her current gig as a co-host of Fox News' "The Five".
She said she believes she has a "good relationship" with the president.
President Trump is reportedly considering a major shake-up in his communications department, and a Bay Area native may be part of his plans.
On this week's show, he said, the cast made light of Trump's interview with Lester Holt, his lawyers' admission that he has no business dealings with Russian Federation "with a few exceptions" and Sean Spicer's combative press briefings.
Last week, President Trump strongly implied that he has recordings of his private conversations with former Federal Bureau of Investigation director James Comey.