The Spanish outfit can claim to have enjoyed a productive first half of the season courtesy of having qualified for the Champions League last 16.
However, their form in La Liga has been mixed, just eight victories coming from their 20 matches and their winless streak standing at four games.
As a result, Imanol Alguacil's side sit in sixth position in the standings, nine points adrift of fourth-placed Barcelona, while they have scored considerably fewer goals than the five teams above them.
Alguacil is now in the market for at least one attack-minded addition, Fichajes claiming that there are three names on the club's shortlist.
Among those is Spurs playmaker Gil, who is currently being handed regular opportunities at the Tottenham Hotspur Stadium without being viewed as a key player.
The 22-year-old has made a total of two starts and eight substitute outings in all competitions, Gil being used off the bench in the most recent four fixtures.
Nevertheless, that is largely due to the selection issues currently facing Ange Postecoglou, and a gap in the schedule leaving Spurs without a game until January 26 could theoretically result in Gil moving elsewhere before the next fixture.
Recently, Fiorentina have been credited as admirers of Gil, but his most productive stints have come back in his homeland with the likes of Valencia and Sevilla.
Gil was a regular for the latter during their Europa-League-winning campaign in 2022-23, and Sociedad are seemingly attracted to acquiring the services of the versatile creator, either on loan or permanently.
The report adds that Txuri-Urdin are also contemplating whether to make approaches for Borussia Dortmund's Giovanni Reyna and Hellas Verona's Cyril Ngonge.
Reyna is out of favour at the Westfalenstadion at a time when Dortmund have under-performed for a number of months, and a loan switch is regarded as a possibility now that Jadon Sancho has arrived from Manchester United.
Meanwhile, Ngonge has contributed six goals and two assists in Serie A during 2023-24 and would allegedly cost in the region of €12m (£10.32m).