For almost two decades, Chelsea had Russian representation in the form of owner Roman Abramovich until a sale of the club was processed earlier this year.
That was a consequence of Abramovich's links to Russian president Vladimir Putin, who ordered a military invasion of Ukraine six months ago.
Although that is not the solitary reason, there are currently no Russian players who are registered to a Premier League club.
However, according to Russian outlet Sport Express, that could change in the future with Chelsea showing an interest in Zakharyan.
The report claims that Chelsea are willing to pay the release clause of the 19-year-old, said to be set at €15m (£12.7m).
Zakharyan has already starred for Dynamo during his short professional career, contributing 13 goals and 16 assists from 52 appearances in all competitions.
The prospect, who is capable of playing in all the positions across the midfield, has already earned four caps for the senior national team.
As far as this campaign is concerned, Zakharyan has chipped in with one strike and two assists from his five appearances in Russia's top flight.
Should Chelsea progress with a deal, it would follow their strategy of signing a wide range of young talent since the takeover of the club.
Under co-owner and interim sporting director Todd Boehly, Chelsea have signed the likes of Chicago Fire goalkeeper Gabriel Slonina, Inter Milan midfielder Cesare Casadei and Aston Villa playmaker Carney Chukwuemeka.
Omari Hutchinson, Zak Sturge and Tyler Dibling have also arrived from Arsenal, Brighton & Hove Albion and Southampton respectively.
Goalkeeper Eddie Beach also signed from the latter of those clubs at the start of July.