The 24-year-old, who has played his entire career to date in his home country, has scored 10 goals in 36 appearances for the Russian national side.
His contract at the Moscow club is due to expire at the end of the season, and according to Russian outlet Izvestia, Arsene Wenger is keen to complete a deal which could cost the Gunners less then £4.5m.
The report claims that Kokorin has been a target of Wenger's since before this summer, and that the two clubs have now opened negotiations with a view to a deal being completed in January.
The paper also alleges that Arsenal held talks with Dynamo in the summer over a move for the forward, but Kokorin's agent previously insisted that just because a deal could not be agreed a few months ago does not mean that his client will not be able to move in January.
According to the Daily Star, Cyril Loginov said in October: "Aleksandr, if all well-informed, still has a chance [to move] and not just to Arsenal. If Dynamo refused to give Aleksandr to Arsenal in the past transfer window, it does not mean that he cannot be where he wants."
Arsenal travel to Aston Villa tomorrow as they look to keep pace with Leicester City at the top of the Premier League table. body check tags ::