Weghorst was taken to Turf Moor in the January transfer window to help Burnley’s battle against relegation from the Premier League.
He was unable to help the Clarets survive and is not keen to play in the Championship next term.
Weghorst would prefer to stay within the Premier League or move to the Bundesliga, but Burnley are close to sending him on loan to Besiktas.
Burnley want a purchase option included in the loan agreement with the Turkish side.
Besiktas have had issues convincing Weghorst to make the switch to Turkey, but are closing in on the deal.
The Black Eagles finished just sixth in the Turkish Super Lig last season and scored eleven fewer goals than champions Trabzonspor.
They will be hoping that Weghorst can add a cutting edge up top as they look to push up the Super Lig standings next season.
