The 2023 Ryder Cup will be played from September 29th-October 1st at Marco Simone Golf & Country Club in Rome.
The U.S.-based PGA Tour has suspended those who joined the rebel circuit.
Yet the DP World Tour, formerly the European Tour, is awaiting a legal hearing in February that will effectively decide whether it can sanction players who defected to LIV, or whether they can continue to compete and qualify for the Ryder Cup.
European Ryder Cup stalwarts Ian Poulter, Lee Westwood and Sergio Garcia are among the players that could miss the biennial team competition between the United States and Europe.
When asked about whether LIV golfers should be considered for team Europe in the future, Faldo told Sky Sports: "They shouldn't be there because they've gone off and you've got to move on."
"They're done. It's a rival tour," added Faldo, who was the all-time record points scorer in the Ryder Cup until he was overtaken by Sergio Garcia in 2018.
"If you work for a company for 20 years and you then leave to go to a rival company, I can promise you your picture won't still be on the wall. You've moved on. Fine, off you go.
"They made that decision and I'm sure they knew it was going to cost them. They were playing the maths game. They were getting a huge chunk of money up front, and they knew it was going to lose them sponsors, but they thought 'I still win'."
Faldo added that the LIV series was a "closed shop" and said the Saudi-backed breakaway circuit was not contributing to the growth of golf.
"That really gets me when they fly across the world to a country that's been playing golf for 100 plus years and say, 'we're growing the game of golf'," Faldo said.
"If they keep saying they want to grow the game of golf, go and take it to new regions. Countries in the early days of being interested in golf now. Try that rather than just trying to antagonise everybody."
Critics say LIV Golf, which is bankrolled by Saudi Arabia's Public Investment Fund, amounts to "sportswashing" by a nation trying to improve its reputation in the face of criticism over its human rights record.
