The Foxes expressed interest in signing the former Kano Pillars player in January but had their bid turned down by the Russian champions.
Slutsky confirmed that an offer of £22.8m has now been tabled by the English Premier League champions.
“The British club offered a bit less than €30m (£22.8m),” Slutsky told Russia’s Match TV.
“A few days ago, Musa approached me and asked, when is (Ranieri) back from holiday. I told him, I am not Ranieri, I do not know.
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“I do not know for sure (if Leicester have reopened talks) because these negotiations are dealt with by the management, but I think the probability is very high.”
Musa scored 18 goals to help CSKA win the league in the just concluded season.