The CSKA Moscow striker has been a long term target for the Gunners, who recently got the opportunity to see the 21-year-old up close during their Europa League quarterfinal tie, in which he scored in the first leg.
Golovin is a coveted prospect in Russia and his talents have not gone unnoticed by his compatriot in Abramovich.
According to Russian outlet, Sport24, Abramovich wants to bring Golovin to Stamford Bridge next season.
It is believed Abramovich's close friend Leonid Slutsky will soon be announced as the new manager of the Eredivisie club.
Golovin has scored six goals and provided 5 assists in 38 games across all competitions this season.