Per the source, the Black Eagles could face competition from the Bundesliga for the striker for has scored twice in Villa’s first three Championship games.
The Istanbul giants are currently on the hunt for a striker to replace Mario Gomez who did not return following the end of his loan deal.
Besiktas are running out of time and with the Champions League group stage football looming they are expanding their search.
Eagles president Fikret Orman is currently in England holding talks with a number of clubs trying to strike a deal for a striker and has turned his attention to Gusted who joined the Championship club while they were still in the Premier League last season for £6 million from Blackburn Rovers.
Besiktas would be able to offer Gusted Champions League football and the prospect of being involved in a title race.