The La Liga club signed Tierney on a temporary deal for the 2023-24 season to provide competition for Javi Galan and Aihen Munoz.
Although the Scotsman made 17 starts and 10 substitute outings across all competitions, he failed to make the desired impact in Spain and once again struggled with injuries.
Tierney has since returned to parent club Arsenal, as Sociedad have decided against activating the option to buy the 27-year-old on a permanent deal.
The San Sebastian-based outfit have since begun their search for a new specialist left-back and have seemingly identified another target from the Premier League.
Sociedad in talks to sign Sergio Gomez
According to journalist Fabrizio Romano, Sociedad have open talks with Man City to sign Spanish left-back Sergio Gomez, with initial negotiations taking place between both clubs.
Romano claims that Gomez is expected to leave the Etihad Stadium this summer and Sociedad 'like' the 23-year-old.
A separate report from Diario AS states that Sociedad's club president Jokin Aperribay and director of football Roberto Olabe travelled to England last weekend to finalise negotiations over a deal for Gomez.
It is understood that both Sociedad chiefs met with Man City's sporting director Txiki Begiristain and 'the foundations were laid for an agreement' between both parties.
Gomez seeking regular first-team football
Gomez joined Man City from Anderlecht for a reported £12m in the summer of 2022 after excelling at the Belgium club formerly managed by Vincent Kompany.
However, Gomez has since struggled to nail down a regular starting place under Pep Guardiola and has started only 14 of his 38 appearances in all tournaments.
The Spaniard featured just 15 times for the Citizens last season and was handed only 47 minutes of Premier League football across six substitute outings.
Gomez was ultimately unable to force his way into City's starting lineup ahead of Nathan Ake or new signing Josko Gvardiol, who both featured regularly at left-back.
Meanwhile, Guardiola has hinted at the possibility of Joao Cancelo - on loan at Barcelona last season - returning to Man City for pre-season.