Russia international Golovin has been linked with a move to a major European side after impressing for his country in their surprise run to the FIFA World Cup quarter-finals.
The 22-year-old has been widely tipped to join Maurizio Sarri's Chelsea, which has already moved to strengthen its midfield options with the signing of Jorginho from Napoli.
It appears Golovin's switch to Stamford Bridge is on the cards, with Chepchugov having wished his team-mate good luck at his next club in an Instagram post.
The goalkeeper congratulated Golovin on joining Chelsea and wished him a "great career".
Time will tell if Chepchugov's post proves accurate, with Golovin also said to be interested in joining Cristiano Ronaldo at Juventus, according to Italian newspaper Tuttosport, while Monaco is another potential destination.