The Egypt international had been in dispute with his loan club over unpaid wages.
However, Besiktas president Ahmet Nur Çebi says the differences have been settled and there is an agreement about pursuing a new loan arrangement for next season.
He said, "The contracts are valid until the end of the league. Elneny, who also thought about not going out to work, had to step back after the briefing of the management.
"Later, the parties met once again and an agreement was reached. Elneny gave up asking for money. In addition, we pushed the button to rent the Egyptian football player next season."