The News of the World says Kenyon will take a new job at Galatasaray if steel magnate Adnan Ozturk wins the presidential elections at the Turkish club next week.
Ozturk said: "This club under Polat is in chaos.
"Galatasaray are well-known throughout the world - but we're not winning trophies and there is a lot of debt.
"We want to change this and do it with professional people. If I do win this election, I'll work together with Kenyon, Kurth and Calzado.
"And with these people, we will wake up this sleeping giant."