The Premier League champions made three signings during the recently concluded transfer window, in the shape of Jack Grealish, Scott Carson and Kayky.
However, only Grealish, who arrived from Aston Villa for £100m, is considered to be a major addition to the Citizens’ senior team.
While Pep Guardiola’s side were keen on signing Harry Kane, they are rated as unlikely to return for the Tottenham Hotspur star in the future.
Manchester City, though, are still looking at ways to evolve the team and Real Sociedad forward Oyarzabal has been identified as a potential recruit.
Oyarzabal has previously been linked with a move to Manchester City and is still said to be a top target for the English champions.
Manchester City director of football Begiristain is claimed to be an admirer of the Spain international and is keen to acquire his services from Real Sociedad.
Oyarzabal, who has scored four goals from four La Liga matches so far this season, has a release clause of around £67m in his contract with Real Sociedad.