The Blues have been strongly linked with the Russia international, and an Instagram post by goalkeeper Sergei Chepchugov hinted that his compatriot is heading to Stamford Bridge.
Chepchugov's post congratulated the midfielder on sealing a move to a "big club" and wished him well at Chelsea, with Golovin's official Instagram account @alex_golovin17 liking the post.
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Golovin scored in Russia's opening game at the World Cup as they beat Saudi Arabia 5-0, playing in four of the hosts' games on the way to the quarter-finals before losing to Croatia on penalties.
The 22-year-old also played in CSKA's group-stage defeats to Manchester United in last season's Champions League and scored at the Emirates Stadium when they lost to Arsenal in the Europa League quarter-finals.