The Blues had agreed a £12.6million deal for the midfielder after the club activated his release clause.
The 19-year-old was expected to make the switch to Stamford Bridge, but he was blocked from doing so, due to the United Kingdom's sanctions onRussia amid the war in Ukraine.
It has been revealed the main stumbling block was transferring the funds to the club based in the Russian capital.
There was also difficulty in him obtaining a work permit from the Home Office.
Further complications would have also come into fruition, after FIFA's rules on signing Russian players following the invasion.
"On August 25 we received an offer fromChelsea
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for Arsen Zakharyan," a statement from Dynamo confirmed.
"For several days, there have been intense negotiations between Dynamo and Chelsea, in which our club took a constructive position.
"However, it is not possible to transfer a player in this summer transfer window for a number of technical reasons beyond our control."
Zakharyan featured 34 times for Dynamo last term, netting nine goals, while contributing to nine assists.
Agent Rafaela Pimenta also toldSport Express: "Today, it is impossible to close the transfer of Zakharyan in the summer transfer window.
"This transfer is not frozen until winter, but it is possible.
"Now we are still working to ensure that Dynamo can get money from Chelsea."
Chelsea did manage to secure the services of Pierre-Emerick Aubameyang from Barcelona on deadline day, and Juventus midfielder Dennis Zakaria.
Meanwhile, Billy Gilmour left the Blues on a permanent deal joining Graham Potter's Brighton.