City have long been linked with a swoop for the 22-year-old, but following a tough start to the Premier League season, Pep Guardiola's men could launch a move next month.
At one point it was thought that all major transfer business would be on hold until the end of the season, but as City sit third in the Premier League standings, way behind leaders Liverpool, new signings are needed now.
Guardiola is keen to get reinforcements on board as soon as possible and is said to have around £100million to spend on new players, with a large chunk of that set to go on Oyarzabal.
The youngster, who has made over 150 senior appearances for Sociedad since 2016, has scored six goals and chipped in with another four assists in La Liga so far this season.
It is form that continues to attract the attention of City and a bid could be in the pipeline.
Oyarzabal is seen as the perfect replacement for City star Leroy Sane, who is expected to leave for Bayern Munich at the end of the season.
The German international is currently out of the City side through injury and has been unable to play at all so far in this campaign.
He has been a big loss to the English side, who feel the capture of Oyarzabal could help fill the void in both the short and long-term.