The Kosovo international has shone for club and country so far this season and attracted the attention of Barca sports chief Deco.
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Sky Deutschland says Deco has been impressed by Asllani, who is tied to Hoffenheim until 2029, with the deal carrying a buyout clause.
For his part, Asllani has welcomed the interest, stating to BILD recently: "My dream club has always been FC Barcelona - I have always wanted to play there."
The striker struck the winner against Sweden on Monday as Kosovo triumphed 1-0 in Gothenburg.