Leicester paid a reported club-record £16 million to sign Musa in July 2016 as they bolstered their squad for a Champions League campaign in the wake of their stunning Premier League title success.
But the Nigeria international only scored two top-flight goals in his first campaign, while his only strike this term came in a 4-1 win over Sheffield United in the Carabao Cup second round in August.
Musa has subsequently been allowed to depart the King Power Stadium until the end of the season.
"Ahmed will be included in the Red-Blues' squad list for the national league and the Europa League knockout stage," said a CSKA statement on Tuesday.
Leicester, who are yet to confirm Musa's departure, on Monday allowed Leonardo Ulloa to go out on loan to his former club Brighton and Hove Albion.