Avanesyan was born in Uzbekistan and moved to Russia at the age of two.[1][2] Later, he joined the junior teams of CSKA Moscow in 2015, and was first included in their Russian Premier League squad in February 2017, but did not make any appearances for the senior squad in the next 4 years, playing only in the youth team.[3]
On 9 June 2022, Avanesyan was loaned to Baltika Kaliningrad, where he already played on junior levels, for the 2022–23 season.[9] On 20 June 2023, Baltika made the transfer permanent.[10]