The 24-year-old only joined CSKA in January from VVV Venlo, helping the Russian side reach the quarter-finals of the Champions League.
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But his impressive displays for his country at the World Cup are believed to alerted several top European sides, including the Gunners, whose boss Arsene Wenger recently revealed his admiration for Honda.
The player’s agent, Kees Ploegsma, admitted that the attacking midfielder would be open to a move to England, but added that breaking away from his current contract with CSKA could prove a significant stumbling block.
"There has been no interest as of yet, only rumours. But obviously he is open to think about everything. The difficulty is that he has just signed a four-and-a-half-year contract at CSKA Moscow and he has only been there for half a year," he told Sport.co.uk.
“Obviously he is open to interest and talk of the Premier League but the second issue is CSKA Moscow. I am not saying it is unlikely that they might sell him, but I don’t know what price they would be asking for as he is under contract for another four-and-a-half years."
He later revealed that Honda would find it difficult to turn down a move to a big European side such as Arsenal, should the Gunners stump up the required about of cash.
"Keisuke plays in a beautiful city for an important club, but obviously if there are offers from big European clubs it is difficult to say no," he said in The Sun.
"At this time there are no bids and all in all he is happy at CSKA, but we'll see."
Speculation linking Honda with a move to Emirates Stadium has arisen following Wenger's comments about the forward during the World Cup.
With a vast knowledge of Japanese football having managed Grampus Eight prior to joining Arsenal, Wenger has clearly been more than impressed with Honda’s input to the team during their recent campaign in South Africa.
“The Japanese team is based on a solid and collective defence in which everybody knows exactly what to do.” Wenger told Eurosport.
“When they get that genius Honda playing up front, he has shown what a top class player he is."
Honda himself has admitted that he would consider leaving CSKA should the opportunity to join a major European outfit present itself, and that, ideally, he hopes to play for Real Madrid one day.
"I dream about wearing the number 10 jersey at Real Madrid. I'm the type of person who always wants the best and I've always had the desire to play at the highest level," he told Sports Nippon.
"If the opportunity comes up to join a bigger club, I'd definitely consider it."
Arsenal have already added to their forward line this summer after bringing in Bordeaux forward Marouane Chamakh, but may be in need of another new recruit with injury-plagued Croatia striker Eduardo being linked with a move away from Emirates Stadium.
By Nick Poyser
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