The Turkish club have offered the 26-year-old a three-year contract worth close to €5m in signing-on fees plus just under €10m per season in wages, and although Vlahovic has already travelled to Istanbul, he has yet to give an answer.
Besiktas' patience is said to be wearing thin as the days pass without a response, with their confidence in landing the Serbian growing shakier by the day. Juventus paid around €75m for Vlahovic when they signed him from Fiorentina, but his time in Turin never matched that outlay, with inconsistent form eventually leading the Bianconeri to decline extending his contract; he became a free agent on 1 July after rejecting a renewal offer worth around €6m a season, roughly half his previous salary.
Vlahovic's reluctance to commit to Besiktas stems from a meeting he has already held with Barcelona sporting director Deco, in which the Serbian made clear his belief that he could fill the void left by Robert Lewandowski's departure to Chicago Fire, as well as any gap that might open up should Ferran Torres leave for Paris Saint-Germain.
Barcelona are aware of the situation, and while Vlahovic knows the salary on offer at Camp Nou would fall well short of what Besiktas are proposing, his desire to play for the Catalan club remains undimmed.
Hansi Flick had wanted a more physically dominant, high-pressing centre-forward in his squad, but Deco and Joan Laporta see Vlahovic's availability as a free agent as an attractive proposition in its own right, since it would preserve the club's financial flexibility even if wages need to be found.
For now, the situation remains stalled, with Julian Alvarez still Barcelona's priority attacking target this summer, but insiders at the Camp Nou believe talks over Vlahovic could be revived depending on how the club's other business develops in the coming weeks.