Arlind Sadiku, a football commentator for Kosovar media company Artmotion who is covering the World Cup from the ground, reported on Friday that Asllani will join Borussia Dortmund and that the transfer has already been finalised.
The Westdeutsche Allgemeine Zeitung moved quickly to dispute the claim, stating no agreement is in place and that a move to Dortmund is not imminent.
Kicker had previously reported that the 23-year-old would very likely leave TSG Hoffenheim this summer, with the club needing to generate transfer income after spending around €35 million on incoming players. Alongside Bazoumana Touré and Muhammed Damar, Asllani is identified by the magazine as a near-certain departure.
The Kosovo international posted 11 goals and 10 assists in 35 competitive appearances last season as Hoffenheim secured Europa League football with a fifth-place finish.
His contract runs until 2029 and contains a release clause fixed at €30 million for clubs that have participated in the Champions League in each of the past three years — a condition Dortmund meet. Reports suggest BVB's current transfer budget sits at around €25 million, making the full clause cost a financial obstacle unless income arrives from player sales first.
Dortmund sporting director Ole Book knows Asllani well, having previously signed him for SV Elversberg where the striker scored 18 goals on loan. The personal connection is considered a significant advantage for BVB in any pursuit.
Recent reports indicate Asllani has held talks with Dortmund's representatives and is very open to the move. The club has stressed that concrete action will follow only once departures from the squad are confirmed.
Should Asllani arrive at Signal Iduna Park, it would likely trigger an exit for one of Serhou Guirassy or Karim Adeyemi, both of whom face uncertain futures at the club. Guirassy's agent has denied a reported agreement with Fenerbahce, saying no deal of any kind has been struck.
RB Leipzig are also tracking the Kosovo international and have held direct talks with his representatives, while FC Barcelona's interest was confirmed by Asllani's own agent several months ago.