The usually shy Slutsky recently revealed that he likes to tease former CSKA midfielder Sergei Semak, a father of seven kids, about naming his next child after him.
"I have this long-time dream that one of my current or former players would name his child after me. Sergei has seven kids so we joke all the time," Slutsky told local media.
"I tell him 'you are my biggest hope'. Maybe one day he would name his next kid after me."
In 2008, many Russians gave their children the unusual Dutch name Guus in honour of coach Guus Hiddink, who led Russia to a Euro semi-final that year.
Whether his dream comes true or not, Slutsky, who turned 42 this month, has already made his mark at CSKA by becoming the youngest coach in the club's history to win the league title.
CSKA sealed top spot with a game to spare thanks to a 0-0 draw against Kuban Krasnodar on Saturday.
Slutsky will have a chance to lead CSKA to their first league and cup double in seven years when they take on Hiddink's Anzhi Makhachkala in the Russian Cup final in the Chechen capital Grozny on June 1.