Slustky, born in Volgograd to a Russian-Jewish family, is in the frame be hired by the Championship club to lead next season's promotion charge.
The 46-year-old is a close friend of oligarch Roman Abramovich. And his connections with the Chelsea owner have helped Slutsky, who has been in England for three months in the hope of sealing his first foray into the dugout, land the job.
"Mr Abramovich is my friend and he is helping me achieve my dream. It's a challenge for him also,” Slutsky said last month.
“He is like my agent, the best agent in the world.