The comedian and show panellist recently walked off the ABC series with co-host Whoopi Goldberg after becoming enraged by comments O'Reilly made about Muslims.
A source told Pop Eater: "Bring it on. Joy isn't scared. She has more balls than Bill O'Reilly will ever have.
"This is a woman who was told she would never have her own show and now she's a ratings queen on HLN. She has had to fight her entire life and if The View want to bring back Bill, Joy will be ready."
However, Goldberg is said to be unwilling to "sit down at the same table" with O'Reilly again.
"Whoopi wants no part in a television battle with Bill. She's way too smart to be fighting on TV with some man full of hate. What does she have to prove?" the insider explained.
"She's got an Oscar on her shelf, a string of blockbuster movies and a Broadway play coming to New York. I'm sure the schedule will make sure that when Bill returns, Whoopi is coincidentally away that day with a prior commitment."