Moscow turned down a new bid of $26.5m (£18.7) which was an improvement on the original offer of $21.6m (£15.1m).
The 23-year-old is believed to be open to a move to Leicester.
The Nigeria captain has also attracted the attention of other top Premier League teams and has a $32.5m (£22.8m) buyout clause in his contract.
His current deal with CSKA Moscow runs until 2019.
Leicester are expected to return with an improved bid for the player before the transfer window closes on 1 February.
A former VVV Venlo player, Musa has scored 10 goals in 29 games this season and 11 times in 56 appearances for Nigeria.
Musa, who made his international debut against Madagascar in September 2010, scored twice in Nigeria's 3-2 loss to Argentina at the 2014 World Cup in Brazil.
He scored the county's fastest-ever goal at a World Cup - netting after four minutes - before becoming their first player to score twice in one game at the tournament.

Ukraine prosecution officials said there was no evidence of a crime but one politician called for the president to face impeachment proceedings.
Eleven million documents from Mossack Fonseca show how some of its clients use it to avoid tax and launder money.
The firm says it did nothing illegal.
The Panamanian firm is alleged to have set up a company in the British Virgin Islands for Mr Poroshenko called Prime Assets Partners, which describes itself as a holding company of the Roshen confectionery group. Before becoming president, Mr Poroshenko had been known as the "chocolate king".
During his presidential campaign in 2014, Mr Poroshenko vowed to sell most of his business assets. He won the election and was sworn in in June 2014. The assets were transferred to the newly created holding company.
In October 2014 a Ukrainian bank, of which Mr Poroshenko owns a controlling stake, sent a letter of recommendation to Mossack Fonseca saying that his accounts had been "conducted properly up to our satisfaction", according to the International Consortium of Investigative Journalists.
Journalists from the Organized Crime and Corruption Reporting Project (OCCRP) argued that President Poroshenko's action might be illegal on two counts: starting a new company while president and not reporting the company on his disclosure statements. The BBC cannot independently confirm this.
Anti-corruption group Transparency International also believed that the "creation of businesses while serving as president is a direct violation of the constitution".
But a spokesman for Mr Poroshenko said the company it set up for the president had no active assets and was part of a legitimate corporate restructure aimed at helping to sell the Roshen group. None of the three associated accounts held more than â‚¬2,000 (Â£1,600; $2,270), he said.
The Ukrainian leader went on Facebook to insist that, on becoming president, he had delegated management of his assets to consulting and law firms.
"I believe I might be the first top office official in Ukraine who treats declaring of assets, paying taxes and conflict of interest issues profoundly and seriously, in full compliance with the Ukrainian and international private law," he wrote.
Legal firm Avellum, which was given the task of selling Roshen, said that using a company with foreign jurisdiction was the only way to move the company into a blind trust. "Any allegations of tax evasion are groundless," it told Reuters news agency.
However, Oleh Lyashko, head of the populist Radical party which had earlier been part of the governing coalition, called for impeachment proceedings to be initiated, although that was unlikely to take place.

Labour had the most councillors on the city council after last week's elections.
BBC Scotland revealed that as well as the Conservatives the coalition will rely on the support of three Independents. Labour's Barney Crockett will be the new council leader.
The SNP and Lib Dems will form the opposition on the council.
A new Independent-Conservative administration will run Moray Council.
The Independent councillor for Keith, Stewart Cree, has been chosen as council convener.
Meanwhile, the leader of the SNP group on Aberdeenshire Council has fought off a challenge to her leadership.
At the group's AGM on Tuesday, Joanna Strathdee was ousted as leader by Rob Merson.
BBC Scotland understands that Mr Merson was in post for about an hour before resigning, to be replaced by the former leader.
The SNP is the biggest party in Aberdeenshire and is continuing negotiations to form a coalition.
Russian club CSKA Moscow have rejected an improved offer from Premier League leaders Leicester City for Nigeria's Ahmed Musa, BBC Sport understands.
[NEXT_CONCEPT]
Ukrainian President Petro Poroshenko says he did nothing wrong, after leaked documents suggested he had set up an offshore company as a tax haven using Panamanian legal firm Mossack Fonseca.
[NEXT_CONCEPT]
Labour and the Conservatives have joined forces to form an administration in Aberdeen.