The girl group announced last month that they will reform for a series of gigs this summer, possibly including The Queen's Jubilee concert in June.
However, Frost has refused to join Natasha Hamilton and Liz McClarnon if Katona also joins the trio, reports The Sun.
Hamilton had previously hinted that Katona could form some part of their reunion plans.
Frost replaced Katona in the group in 2001 after Katona fell pregnant, and just before they experienced their first big success with 'Whole Again'.
Manager Martin O'Shea is said to be trying to work out a compromise deal.
"The claws are really out. Jenny is furious the reunion seems to be all about Kerry," a source said.
Kerry Katona recently said that it would be "good fun" to tour with Atomic Kitten later this year.
Atomic Kitten were originally rumoured as this year's UK entrant for the Eurovision Song Contest, before Engelbert Humperdinck emerged as the chosen artist.
Jenny Frost was recently replaced by Ellie Taylor as host of BBC Three's Snog, Marry, Avoid?.
Watch the Atomic Kitten 'Whole Again' music video below: