After Austria's Klien impressed in the first three grands prix of 2005, Liuzzi - an F1 rookie - tried his hand at Imola, Barcelona and Monaco.
"After Sunday we will make a decision," team principal Christian Horner revealed at Monaco.
The Red Bull chief rejected the notion that Klien, 22, appears the stronger of the pair.
Horner insisted: "For a rookie (Liuzzi has) done an excellent job, and (Christian) is champing at the bit to get back in."
Meanwhile, Red Bull regular David Coulthard vowed to 'drop my pants' if he wins a third career Monaco grand prix.
He also claimed that McLaren 'replacement' Juan Pablo Montoya is not doing 'a significantly better job (than me).' -gmm