The 20-year-old forward, who is yet to make a first team appearance for the Reds, has signed a contract until the end of the season.
"I hope we can win the championship. This is important for us an for the fans. I am coming to a big club in a great city," the Under-21 international said. "The level of the Greek championship it good and I'm looking forward to it."
Born in Gyor, Nemeth started his career at hometown club Gyori where he played from 2003-05 as a youth player.
In 2005, he signed for MTK Hungaria, with whom he scored 18 goals in 37 league games and helped the club to finish second in the Hungarian National Championship in 2007.
Later that year, he signed a three-year contract with Liverpool alongside striker Andras Simon, who has been loaned to Spanish side Cordoba CF for the remainder of the season.
Last week, Liverpool signed Greek international defender Sotiris Kyrgiakos from the Athens club.
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