That is according to the Daily Mirror, who claim the Foxes are prepared to meet the Nigeria international's £22.8million release clause to land him.
The Premier League leaders made a number of bids for the 23-year-old in January - the latest believed to be £18.7m - but they were all turned down by CSKA.
Manchester United have also been linked with a move for Musa, who has 10 goals to his name this term, and are thought to be keen on securing his services ahead of next season.
But Leicester boss Claudio Ranieri is reportedly desperate to get there first as he prepares for the likelihood of Champions League football next term.
Musa's agent revealed last month that pacey striker would be interested in a move to the King Power Stadium, but only if Leicester tabled a big move.
Tony Harris said: "Playing in England is tempting for each player, and Musa is no exception. He would willingly go there. If there is a suitable offer, he would certainly consider it."