The Blues have been in the market for some of Europe's most highly-rated prospects so far this summer since the arrival of new chairman and co-controlling owner Todd Boehly.
Eighteen-year-old midfielder Carney Chukwuemeka has arrived from Aston Villa for a fee which could rise to £20m, while 19-year-old Cesare Casadei has joined the club from Inter Milan in a deal worth €15m (£12.7m) plus €5m (£4.25m) in add-ons.
Goalkeeper Gabriel Slonina is another teenager to move to West London, with Chelsea spending around £8m on the 18-year-old and sending him back to Chicago Fire on loan, while Omari Hutchinson, 18, has joined from London rivals Arsenal on a free transfer.
A recent report claims that Chelsea have expressed their interest in signing Zakharyan and are willing to activate his release clause, believe to be worth €15m (£12.7m).
However, the attacking midfielder's agent Rafaela Pimenta has confirmed that his client will remain with Dymano Moscow this summer.
"Today, it is impossible to close the transfer of Zakharyan in the summer transfer window," Pimenta told Sport-Express.
"This transfer is not frozen until winter, but it is possible. Now we are still working to ensure that Dinamo can get money from Chelsea."
Since making his professional debut in October 2020, Zakharyan has developed into a first-team regular for Dynamo Moscow and enjoyed a productive spell in front of goal last season.
The four-cap Russia international scored nine goals and provided nine assists in 34 appearances for Dynamo across all competitions and helped the Belo-golubye finish third in the Russian Premier League.
Zakharyan, who has two years remaining on his contract, has since made a bright start to the new campaign, contributing to three goals in six top-flight appearances.
With Zakharyan now set to stay with Dynamo, Chelsea can focus fully on their pursuit of Barcelona striker Pierre-Emerick Aubameyang, with one report claiming that they have reached an agreement with the Catalan club to sign the 33-year-old for €14m (£12.1m).
The Gabon international, who only arrived at Barca on a free transfer from Arsenal in January, is set to sign a two-year deal at Stamford Bridge and reunite with head coach Thomas Tuchel, who he spent time with at Borussia Dortmund.