The 32-year-old failed to make a single appearance for the Gunners in the first half of the 2020-21 campaign before being allowed to leave the Emirates Stadium on a free transfer.
A number of clubs, including Genoa, have been linked with the centre-back, who has been capped on 90 occasions by Greece.
However, according to Gazzetta dello Sport, Lazio have won the race for his signature, with Sokratis expected to sign an 18-month contract with the Italian giants.
The report claims that the club's need for a new centre-back was strengthened when Luis Felipe was forced to undergo ankle surgery, effectively ruling him out for the next couple of months.
Sokratis made 69 appearances for Arsenal after arriving from Borussia Dortmund in 2018.