A £125m signing from Bayer Leverkusen, Wirtz has failed to catch fire in his first five months in England.
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Speaking on Sky Deutschland, Hamann said: "Christmas is approaching and he still hasn't scored a goal or decided a match. Football is played differently in the Premier League, and he's had little to no impact there so far.
"Liverpool signed a player for €140 million hoping he could turn around a struggling team with one or two plays. He still hasn't done that, and why would he now in January?
"When I watch him play, I sometimes get the feeling that he himself no longer believes in his potential. Wirtz made the wrong choice in the summer when he was faced with the choice between Liverpool and Bayern Munich."