The '90s girl group are rumoured to be reforming for the ITV2 series, and Redknapp was previously thought to be on board.
The singer, who launched a successful solo career after leaving the band in 1995, was said to have signed a deal worth £500,000 to appear on the show and take part in a subsequent arena tour.
However, fresh claims in The Sun state that Easther and Vernie Bennett and Kéllé Bryan will reunite without her after she decided to focus on her family life with husband Jamie Redknapp.
Louise, who has moved into TV presenting in recent years, previously said: "I wouldn't be upset at all if the girls wanted to reunite without me.
"It would be fun, but if Eternal were ever to get back together it would be a new song with a real purpose rather than just a TV thing."
5ive, B*Witched, Atomic Kitten, Honeyz, 911 and Liberty X all participated in the first series of ITV2's The Big Reunion. A second run is planned for next year.
Watch Louise's video for '2 Faced' below: