Abramovich, who has owned Chelsea since his takeover in June 2003, sees him as a "project" to improve the reputation of Russian football., though, Slutsky he could soon resume his managerial career.
"He is my friend and he tries to help me in the situation," the 46-year-old Slutsky told the BBC.
"I have studied English and watched a lot of football matches. Not only Premier League, but also Championship and League One.
"He had an academy in Russia, invested a lot for infrastructure in Russian football. He built about 300 artificial pitches and was sponsor of the Russian national team. Today, his project in Russian football is me."
Hull have been seeking a new head coach since the departure of Marco Silva following the club's relegation from the Premier League, with the Portuguese succeeding Walter Mazzarri at Watford, and Slutsky is reportedly a front-runner.