The former Gor Mahia striker has been linked with a transfer move to the Istanbul giants this window
The towering Olunga, who currently turns out for Japanese side Kashiwa Reysol, is the leading goal scorer with nine from eight matches in the J-League.
“Olunga, who transferred to Kashiwa Reysol in 2018 is being monitored by Besiktas and could be signed this transfer window,” the reports stated.
Olunga signed for Reysol on a two-year deal worth Ksh300million two seasons ago, a deal that saw him earn more than Ksh15million per month, making him the first Kenyan footballer to professionally play in Japan.
The deal to Reysol saw Olunga end a loan spell with Spanish side Girona and also terminate a contract with top Chinese club Guizhou Zhicheng.
In a recent interview, former Gor Mahia coach Dylan Kerr told Goal how he almost sealed a transfer for Olunga to England.
“But that is it because he already decided to go to Japan, it was to happen two years ago but now the deal could not be sealed because he opted to sign in Japan.
“It was to happen at [Bolton], I got a chance for him at Bolton but he went to Japan, that is it, nothing much to say, I know [Olunga] is happy he went to Japan, he chose Japan for his career.
“Bolton would have loved to have a look at him but he was signed by Reysol, so whilst Bolton would have invited him, he had already picked his destination as Japan, I don’t think this is a story, because it never happened anyway.”
Asked on how he managed to secure a trial for Olunga at Bolton, Kerr explained: “It was a conversation I had with my friend as I do for many players I know could add value to a team.
“I’ve recommended players to may clubs that I believe they can add value to their teams all over the world, but then that is all I can do, my work is to recommend then the club can act, and it was the same case with Olunga.
“I’ve recommended [Olunga] and other players to people I know and who trust my opinions in the game across Asia, America, and Europe.
“Just recently, a team in the USA asked my opinion on Kenneth [Muguna] of Gor Mahia and I told them I think he can be a good acquisition to any squad, I am always asked by agents for African players to play even in Asia.”