The 19-year-old has established himself as one of the brightest young prospects in Europe following a breakthrough 2021-22 campaign which saw him score nine goals and create nine more in 34 appearances across all competitions, as well as winning four caps for Russia.
The Dynamo Moscow midfielder was set to move to the Blues during the summer transfer window, but western sanctions on Russia in light of the latter's military invasion of Ukraine earlier this year prevented Chelsea's new owner Todd Boehly from transferring the necessary funds to finalise any deal.
Zakharyan has since admitted that he was keen on a move to Stamford Bridge, and Chelsea are expected to revive their interest in the youngster when the transfer window reopens in January.
However, Spanish outlet Fichajes claims that Barca and Real are ready to pounce should the player develop any change of heart in the coming months.
Chelsea's interest in Zakharyan signifies Boehly's grand spending and ambition since succeeding Roman Abramovich as the club's owner earlier this year, having spent over £250m during the summer transfer window.
Despite bringing established players such as Raheem Sterling, Kalidou Koulibaly and Pierre-Emerick Aubameyang to the club, there has been an emphasis on youth too, with teenagers Carney Chukwuemeka and Gabriel Slonina joining from Aston Villa and Chicago Fire respectively.