The 31-year-old has made just three Premier League starts for Jurgen Klopp’s men so far this season.
Klavan has also made two appearances in the cup competitions for the Reds, who have been widely criticised for their instability at the back in the current campaign.
Liverpool are currently seventh in the Premier League ahead of the impending clash with Jose Mourinho's Manchester United on Saturday (12:30).
Klopp's team have conceded 12 goals in the top flight so far this season, more than any team above them in the Premier League.
And Arsenal legend Wright admits that he is yet to be convinced by Estonia defender Klavan.
Speaking to BBC Radio 5 live, Wright said: “The defensive errors have been continuing.
"Why hasn’t he [Klopp] addressed the defensive problems?
“Matip is OK but Klavan I’m not sure about.”
But Wright defended Klavan 12 months ago saying: “You’ve got a new centre-half but he still has to get used to who he is playing with and the system.”
Clearly the former England striker was expecting an improvement in the centre-backs's defending that he is yet to see.
The Reds, who finished fourth last term, are currently seven points behind leaders Manchester City after seven games of the new campaign.
