Sports.ru says the Gunners are on the brink of a €11.5 million deal with CSKA for the 21 year-old.
With Leonid Slutsky confirmed as new Hull City manager, the former Russia coach is expected to welcome Golovin on-loan to the Championship for next season.
High profile agent Sandor Varga is backing the deal.
Varga insisted: "Arsène Wenger likes to take young players to develop. Golovin has a lot of potential and would be able to get a foothold in at Arsenal."
However, former Russia international striker Sergei Yuran warns, "It's too soon for him to go to England. He's not ready."