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The 17-year-old moved to Anfield last summer and has been playing for the Under-18s under Marc Bridge-Wilkinson.
Musialowski has made a strong impression since joining from SMS Lodz, with a solo goal against Newcastle named Premier League U18's Goal of the Season.
The winger has notched up 12 goals and three assists in 25 appearances.
A statement on the club's official website read: "His ability to travel with the ball and dribble past defenders soon caught the eye.
"He scored his first goal for the club in November, against Leeds United at Melwood, and finished the season with 10 to his name.
"That included a fine effort at Anfield against Arsenal in the FA Youth Cup quarter-final, a competition in which Musialowski also scored in the semi-final against Ipswich Town as the Reds reached the final."
Musialowski has reportedly signed a three-year deal and is spending time with Jurgen Klopp's first-team squad during pre-season in Austria.