The fee for the Nigerian international is in the region of 16 million pounds ($21.20 million) according to British media reports, which would be a club record.
"Everything has been finalised and Musa will be in England for his medical on Wednesday," the player's agent Tony Harris told BBC Sport.
CSKA Moscow coach Leonid Slutsky was also optimistic that Musa would flourish in England.
"He'll be leaving on Tuesday," Slutsky told Russian media.
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"If you look at the way things are done over there, you'll see he is a player just made for English football."
Leicester City also announced the signing of midfielder Nampalys Mendy from Nice on Sunday.
($1 = 0.7548 pounds)
(Reporting by Nivedita Shankar in Bengaluru; Editing by John O'Brien)
