The much-admired playmaker enhanced his reputation with a string of impressive displays for his country at the World Cup last month, scoring twice and setting up another goal as Japan reached the last 16.
And after ongoing talks between the two clubs in the last 24 hours, the Rossoneri are believed to have matched CSKA's valuation - in the region of €15 million - and are confident of sealing the switch for the 24-year-old in the coming days.
"We are very close to signing Honda, the clubs are very close to finding an agreement," a source close to the Milan club told Goal.com.
Honda has been the subject of intense speculation following a whirlwind seven months in Russia after starting last season in the Dutch second tier with VVV Venlo before joining CSKA for £5 million last December.
He won many admirers after starring for the Russian outfit in last season's Champions League and at the World Cup, with Emirates Stadium chief Arsene Wenger hailing the Japanese sensation as his player of the tournament in South Africa.
"When they [Japan] get the ball they can give it to Honda - and the magic starts," Wenger told Eurosport earlier this month.
"When they get that genius Honda playing up front, he has shown what a top-class player he is. For me he's the best performer of the competition."
Honda, who can play on either wing or as a second striker, has seen his stock rise in 2010 and has stated his dream is to wear the No.10 shirt for Real Madrid after being linked with moves to some of Europe's elite clubs in England, Spain and Italy.
Arsenal have already added to their forward line this summer after bringing in Bordeaux forward Marouane Chamakh, but the Gunners may now be on the lookout for another new recruit after Croatia striker Eduardo departed Emirates Stadium for Shakhtar Donetsk.
By James Martini
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