Alioski ended a four-year spell at Elland Road last summer as he decided to not sign on fresh terms at the club following the expiration of his Whites contract.
The North Macedonian joined Saudi Arabian outfit Al Ahli following his Leeds exit, but is now available for a transfer with his current side having suffered relegation last term.
Alioski’s agents have offered him to Turkish giants Besiktas as he looks to return to Europe.
And according to Turkish journalist Mustafa Ozgur Sancar, the Super Lig giants have reached an agreement with the ex-Leeds man over a move.
The left-back is set to arrive in Istanbul on Tuesday to sort out his move to Besiktas following a season in the Middle East.
It has been suggested that Leeds could even look to bring Alioksi back to Yorkshire this summer given left-back Junior Firpo is facing a spell on the sidelines owing to injury.
But the former Elland Road favourite is now set to have his first taste of Turkish football.