The director is overseeing a follow-up to the 1997 action film and hopes the two stars will return as FBI agent Sean Archer and terrorist Castor Troy to provide a "definitive continuation" to the original.
"To me, Face/Off isn't about a procedure or anything like that," Adam told Showbiz CheatSheet. "It's not about the world that the characters exist in. It's about Sean Archer and it's about Castor Troy. That's what this movie is about. It's the continuation of that story. It's hard to talk about other than that but this is, to me, the definitive continuation of that saga."
The "Godzilla vs. Kong" director revealed Travolta and Cage are interested in the project, but they are holding out for a script, which is being written by Wingard and Simon Barrett.
"We're still writing the script so it's still in early phases," the director adds. "Simon and I are very close to turning in our draft to Paramount soon. We'll have to get over those hurdles of, 'Do they like this movie?' They've read our outline. Everybody's on board with it but actually turning in the script's a different thing, so we'll see how everybody reacts to it."
The original movie, directed by John Woo, revolved around Archer's all-consuming mission to catch Troy, the man who killed his son. Taking going undercover to the extreme, Archer undergoes cutting edge facial transplant surgery, so he can take on the identity of Troy and head into prison to prevent another attack after the criminal falls into a coma.
However, Troy unexpectedly wakes from his coma and takes on Archer's face, which leaves the real agent desperate to stop his nemesis and reclaim his face and life.
Wingard insists the two characters will be at the centre of the plot for the new movie.