Golovin has been the standout player in a Russia team who shocked the world by knocking out Spain, and naturally this has caught the eye of Roman Abramovich.
However, as Chelsea put together a €30million deal, they face stiff competition from Juventus who have also shown an interest.
However, the west London side are keen to move quickly on this deal, as they feel they have already lost time with the protracted negotiations needed to release Sarri from his contract at Napoli.
In addition, new Premier League rules mean that the transfer window will close on August 11th, giving clubs little over six weeks to complete any further deals.
It's because of this that the club are hoping to get ahead and put a bid in with CSKA Moscow as soon as Sarri signs, despite the fact that no deal with the player can be reached until his involvement in the World Cup is over.
So far, Golovin has scored once and provided two assists in the tournament, and scored his penalty past David de Gea in the shootout that saw Spain exit.