The Swiss midfielder has started six games for the London club this term and is rated highly by manager Martin Jol.
His impressive displays have alerted Juve, who are believed to have been aware of the 21-year-old for some time.
Prior to his move to Fulham, Kasami played for Serie A side Palermo, where he developed a reputation as on of the division’s most promising youngsters.
Despite interest from a number of more illustrious clubs, the versatile midfielder elected to join the Premier League side in a £5m deal in 2011.
Juve are now ready to lure him back to Italy with the chance to compete for silverware on a regular basis.
Jol is thought to be keen to keep Kasami, but knows that he may be unable to convince him to reject the chance to move to one of Europe’s top club sides.
The starlet is yet to make a senior appearance for his home nation, but did represent them at the Olympic Games last summer.
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