The Blues had agreed a £12.6m deal to sign the Russian in the summer but the deal broke down due to the FIFA and UEFA restrictions on signing Russian players.
Zakharyan had previously been linked with a move to Barcelona and Real Madrid, but the latest news reportedly points towards a move to Stamford Bridge in the future.
Despite Chelsea's struggles to sign the 19-year-old, the situation looks more promising as Zakharyan has reportedly applied to change his citizenship from Russian to Armenian, in order to force a move to England.
It is claimed that Chelsea are ready and willing to meet his release clause as early as the January transfer window.
Zakharyan has played 17 games in all competitions so far this season, recording three goals and five assists as Dinamo Moscow sit seventh in the Russian Premier League.
Furthermore, he also featured at youth level for his country and has gone on to earn four caps for the senior team.