Golovin has been increasingly linked with a high profile move as a result of his performances at the World Cup on home soil and it was recently reported that CSKA had doubled their price tag.
Juventus and Arsenal were two of the sides apparently interested. But, according to Goal, Chelsea have 'stolen a march' on the Serie A champions and their Premier League rivals after 'making progress' during a meeting with Golovin's agent.
It is said that Chelsea, whose managerial situation ahead of next season is still not entirely resolved, have made it clear to CSKA that they will get much closer to the €30m (£26.6m) asking price than the €20m (£17.8m) bid already tabled by Juventus.
What also promises to hold Juventus back is concerns from Golovin's agent,
"Juventus' interest in Golovin is quite understandable and it's time for him to go to Europe, but not in Italy,"
After a slow start to their summer, Chelsea are now thought to be closing in on the signing of Juventus centre-back Daniele Rugani in a £35m deal. However, the player's agent has warned that things can only become 'concrete' once Maurizio Sarri has formally been appointed.
"It's obvious to say that the Sarri issue must be resolved first. After that, we can proceed with the negotiations and make them more or less concrete," Davide Torchia has told the Italian media.
Such is Chelsea's apparent new found momentum in the transfer market, there has even been gossip that the west London club are making a serious attempt to land coveted Roma goalkeeper Alisson Becker, who has been very heavily linked with Real Madrid and Liverpool.