Asllani, 23, scored 10 goals and contributed 11 assists in the Bundesliga last season for TSG Hoffenheim and carries a release clause of around €30m.
He has repeatedly said playing for Barcelona would be a "dream," and this week published photographs of himself as a child wearing a Barcelona shirt at a ground in Berlin alongside recent images of the same location — captioning them "Same place, different moment."
Barcelona have been monitoring the Kosovo international as a potential plan B should their pursuit of Julián Álvarez from Atletico Madrid prove unresolvable. The Spanish club's sporting management holds positive reports on Asllani and see him as a cost-effective option for the centre-forward position — significantly cheaper than Álvarez, Harry Kane or Eli Junior Kroupi of Bournemouth.
Multiple reports suggest Dortmund have made the most advanced move, with the German club on the verge of agreeing the transfer at around the €30m release clause figure.
Whether Barcelona will move before Dortmund formalise the deal — or whether Asllani's open admiration for the Catalan club can change the course of negotiations — will become clearer in the coming weeks.
Asllani's social media activity may be calculated, instinctive or simply personal sentiment — it is impossible to know which from the outside. What it does is keep his name linked publicly to Barcelona at a moment when the Catalan club are actively searching for a striker and Borussia Dortmund are close to cutting off that option.
If Dortmund complete the signing at the release clause figure, Barcelona will need to redirect their attention to other plan B options. If they move quickly enough to intervene, they would be signing a player who has made no secret of where he wants to play.