Leicester have already had one bid for the rapid forward rejected, but CSKA are reportedly willing to listen to offers.
The Russian club are looking for £19 million for the 23-year-old, which is £5 million more than Leicester’s first offer.
The Foxes do not want to stretch to CSKA’s full asking price, but they believe that a compromise could be met.
Claudio Ranieri believes that that addition of Musa would be vital for Leicester, as they look to consolidate their place in the top four.
The Nigerian international has scored 46 times in 153 appearances for CSKA Moscow, and many of these displays have been as a winger.
Musa also already has over 50 caps for his country, despite still only being 23, and he would become Leicester’s record signing if he does move to the King Power Stadium.