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.
“His new project in Russian football is helping me with my career in England. He's giving me lots of advice about tactics and behaviour and communication with chairmen and owners.”
Slutsky has been out of work since leaving CSKA Moscow last December. His previous job was with the Russian national team. He plotted Russia's 1-1 draw with England in last summer's European Championships but resigned after failing to progress from the group stages, culminating with a 3-0 defeat against Wales.
Dimitry Federov, a Russian journalist who covers CSKA, claimed that the fans turned against Slutsky out of antisemitism after he appeared in a commerical for the Moscow Jewish Cultural center last year.
He said: "Protests against Slutsky stemmed from his appearance in the advert. The fans leading the protests were on the extreme right. They wanted an explanation from him about the ad but he refused, feeling that you don't have to explain things like that."