The Foxes have been after the Nigerian for much of the winter transfer window and were believed to be prepared to part with £15million for his services.
However, CSKA want closer to £19m which is testing the resolve of the East Midlands club who are searching for backup for leading scorer Jamie Vardy and may not want to part with so much money.
Additionally, Musa's agent Tony Harris suggested his client is unlikely to leave Russia this month and is prepared to be patient before he lands a move to one of Europe's top leagues.
"There is little time left in the transfer window," Harris told Russian media outlet Sport Express.
"We are waiting for developments. Sometimes the situation is changing in the last few hours. But Ahmed will most likely remain in Moscow.
"Playing in England is tempting for each player, and Musa is no exception. He would willingly go there. But it is necessary for his club to agree to the proposed terms.
"However, there is no urgency. Ahmed is happy in Moscow. But if there is a suitable offer, he would certainly consider it.
"I can only say that the interest is from a number of clubs, not just Leicester. Once a proposal is acceptable to all parties, we will consider it."