The French side have already contacted CSKA after preparing the transfer money for 25-year-old Honda, who helped Japan to the last 16 at the 2010 World Cup and to the Asian Cup title last year, the Sports Nippon said, quoting PSG sources.
PSG attempted to acquire Honda in the middle of 2011 but a transfer did not materialise as the Russian side set a fee of 25 million euros, the daily said.
Honda's contract with the Moscow team will expire in January next year.
PSG, owned by Qatar Sports Investments (QSI), have used their huge wealth to lure big names and were linked with former England captain and global mega-star David Beckham, who has reportedly turned them down for family reasons.
Sources close to QSI have told AFP in Paris that they have sanctioned bids totalling 61.5 million euros for AC Milan forward Alexandre Pato and Real Madrid playmaker Kaka.
Several major English clubs including Liverpool, Arsenal and Aston Villa were reported to have shown an interest in Honda during the Asian Cup in January last year when he was named the event's most valuable player.
In June, Juventus reportedly held talks with CSKA Moscow over the midfielder.
After four years at J-League powerhouse Nagoya Grampus and two years at Dutch club VVV Venlo, Honda joined CSKA in January 2010 and became the first Japanese player to reach the quarter-finals of the Champions League.
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