Honda has impressed since his move from Dutch side VVV-Venlo last January, netting six goals in 36 appearances for the club.
The Gunners were linked with the 24-year-old last summer following his exploits for Japan at the World Cup, while Roy Hodgson was thought to be monitoring the Japanese international before he was sacked by Liverpool this month.
In an interview in the New Year 2011 issue of FourFourTwo magazine, Honda said: “If I get the chance I would want to play in England. Zoran Tosic and Mark Gonzalez [both team-mates at CSKA] played for Liverpool and Manchester United and I ask them about the Premier League.
“And I’m confident I could play for Real Madrid. But I need good luck to get such a move.”
Honda is currently playing for his country in the Asian Cup in Qatar and scored in the 2-1 win over Syria on Thursday.
After the tournament he will travel back to Russia, a country and culture he has struggled to adapt to.
“When I left VVV it was difficult to adjust to life here. I can’t speak Russian. I know a little bit of Spanish, a little Portuguese, a little English, but not Russian!
“I don’t have any Japanese friends here. But I have my wife here, and my dog.”
Emirates Stadium supremo Arsene Wenger is unlikely to make a move for the midfielder in January with the Gunners well stocked on midfielders, including Cesc Fabregas, Jack Wilshere, Samir Nasri, and Denilson.
However, a summer move for Honda could be in the offing, particularly if Barcelona resume their pursuit for Gunners' captain Fabregas.
Liverpool are believed to be close to capturing the signature of Ajax goal-getter Luis Suarez as new boss Kenny Dalglish attempts to revitalise the fortunes of the ailing Anfield outfit.
Any deal for the Reds involving Honda, though, will also have to be approved by Liverpool's Director of Football Strategy Damien Comolli.
The February - and 200th - issue of FourFourTwo is out now and features exclusive interviews with Dennis Bergkamp, Jurgen Klinsmann, Lionel Messi, Ryan Giggs, Romario, Ronaldo and Alan Shearer. Subscribe here
By Joe Whitbread
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