Racing 'advisor' to team owner Dietrich Mateschitz, Helmut Marko, is thought to have accepted the wisdom of installing more lineup stability.
Liuzzi, the Italian rookie, will thus drive a fourth successive race at the Nurburgring, while Klien resumes the role for Montreal.
22-year-old Klien reported 'disappointment, but not anger,' at Red Bull chiefs' call.
Marko, meanwhile, is thought to have scheduled the next driver decision for after July's Silverstone race, even though - publicly - the seat beyond Canada appears still open.
Liuzzi, who won his first (Formula Renault) car race at the Nurburgring, called the circuit 'one of my favourites.'
"After three grands prix," said the F3000 champion, "I feel I have gained a lot of experience."