The giant Frenchman has been playing in his preferred role of central defence for the last three games in the absence of the injured Stephane Henchoz and he is keen to keep the Swiss star on the sidelines when he returns to fitness.
Traore has impressed in Henchoz's absence alongside Sami Hyypia and was voted Man of the Match in the Premiership win over Bolton earlier this month.
The 23-year-old is hoping to put in another good showing against Celtic in Thursday's Uefa Cup clash after his superb performance in the first leg and prove to Houllier he deserves to stay in the side.
Traore, who was the subject of interest from rival clubs in the summer, revealed he wants to repay Houllier's faith in him and insisted to Liverpool fans that they have not seen the best of him yet.
"Liverpool fans have not seen the best of me and I just want a run of games to prove to them I am good enough," Traore told Planetfootball.
"I know a few clubs wanted to sign me last summer, but Gerard Houllier told me he wanted to keep me and I want to reward his loyalty in me.
"My priority is to be in the first team as I just want regular football at Liverpool.
"I love the club and I love the supporters.
"I want to be playing regularly in the side at this stage of my career.
"I am playing to stay in the side and I want to make it as difficult as possible for Stephane to get back into the side once he is fit."
Traore, who has been used at left full back as well as a centre back this season, admitted his preferred position is at the heart of the defence, but he is happy to play anywhere to stay in the team.
"My real position is the left-sided central defender and I am happy where I am playing now," added Traore.
"I have been asked to play at left back and I have no problem at filling in as I just want to play.
"I love playing with Sami Hyypia in central defence and I am learning a lot off him."
