The Turkish international is said to remain on Everton's radar.
Kerim Frei in Europa League action
According to reports in Turkey Everton are looking into the signature of 22-year-old Besiktas attacker Kerim Frei.
Sporx are reporting that Everton are continuing with a planned bid from Roberto Martinez, who was sacked before the end of last season.
Besiktas' Kerim Frei in action
Ronald Koeman has reportedly decided that Frei is worthy of pursuing and Besiktas are said to be willing to sell the player for a fee in the region of €7 million (£5.9 million).
Frei will be a name familiar to some English football fans. He spent three years at Fulham as a youngster and also spent a short stint out on loan at Cardiff City.
Stewart Downing in action against Kerim Frei
The Austrian-born son to a Turkish father and Moroccan mother was raised in Switzerland – for whom he represented up until under-21 level.
However, since leaving Fulham for Besiktas in 2013 he has represented Turkey at international level and has five caps for the senior national team.
Ex-Everton manager Roberto Martinez
The winger would be a shrewd move from Everton if he can live up to his potential and at the price being quoted would be a bargain.
Everton are certainly in need of another wide option and Frei could easily play from either side of the pitch.