The Auxerre defender has been a long-term target for Houllier, but it appears that Rangers have stolen a march on their rivals by agreeing a deal to sign the French ace on a free transfer next summer.
Boumsong has admitted that he has resisted overtures from Liverpool, Arsenal and Internazionale to agree a deal with Rangers.
Houllier is upset at Boumsong's decision and admitted he is ready to drop his interest in the French international.
"If that is the case and Jean has made those comments, then he is not the type of player for Liverpool Football Club," said Houllier.
"We have shown an interest in Boumsong, but I want players who are happy to play for Liverpool, players who have a desire to pull on the red jersey.
"If he does not have that desire, it suggests he does not have the commitment to play for Liverpool."
Missing out on Boumsong would be a major blow for Houllier as he earmarked the powerful defender as one of his major signings for next season.
