The Russia international has lit up the World Cup and been linked with major clubs across Europe.
However, Gazzaev is convinced Golovin will move to Chelsea once the tournament is over.
"Golovin himself will decide which club is best for him," Gazzaev told Sport. "As far as I know, he has already signed a contract with Chelsea.
"I think it's a good option for him. It is a big responsibility, but he is ready."
It's been suggested Golovin will join Chelsea for a fee in the region of €30m.