Torres, who scored the winning goal in Spain's World Cup final victory over Argentina just over a week ago, has only a year left on his contract at Camp Nou, and the two sides have yet to agree on an extension. Paris Saint-Germain have emerged as the club most strongly linked with the forward, though Real Madrid and Liverpool have also been credited with interest as his situation drags on.
Torres scored 21 goals and provided three assists in 49 appearances, 31 of them starts, for Barcelona last season.
Asllani, 23, is tied to Hoffenheim until 2029 but carries a release clause of around €29 million. The Kosovo international has recently been closely linked with a move to RB Leipzig, and had appeared close to agreeing terms there, but is now reported to be holding out in the hope that Barcelona come calling instead. He scored 10 goals and provided nine assists in 33 Bundesliga appearances last season.
Barcelona's top priority in attack remains Atletico Madrid's Julián Álvarez, though Atlético are doing everything they can to keep hold of their star forward.
Asllani would arrive primarily as a rotation option rather than a direct replacement for Robert Lewandowski, and his potential arrival is specifically tied to a Torres departure rather than forming part of Barcelona's central attacking plans regardless of what happens with the Spain international.
Standing at 1.91 metres and capable of finishing with either foot, Asllani has developed steadily through loan spells at Austria Vienna and Elversberg before establishing himself at Hoffenheim, and his release clause is not viewed as a significant obstacle to any move.
Barcelona could complete a deal without needing to sell Torres first, though the club would prefer to negotiate a lower fee than trigger the clause outright. Time is a growing factor in the situation, with Leipzig pushing hard to finalise their own agreement and reportedly unwilling to wait indefinitely while Asllani continues to hold out for Barcelona to make their interest concrete with a formal approach.