Asllani has been linked with Barca this season and now his agent, Ayman Dahmani, has confirmed contact with the LaLiga giants.
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"Barcelona's interest in the player is genuine at the moment, and there has been contact with the Catalan club," he told Mundo Deportivo.
Hoffenheim is reluctant to sell Asllani this summer - but a buyout clause in his contract could make it impossible for the club to resist.
The clause is said to be worth between €25-29m and it remains to be seen whether any club chooses to activate it.
Asllani's contract with Hoffenheim runs until the summer of 2029.