The Premier League champions are believed to be on the lookout for a new left-back this summer, with Oleksandr Zinchenko edging closer to joining Arsenal for around £30m.
Cucurella is understood to be Pep Guardiola's primary target, although the Citizens are currently unwilling to meet Brighton's £50m valuation of the 23-year-old.
While City remain hopeful of adding Cucurella to their ranks, it is thought that they have drawn up a list of possible alternatives if they are unable to bring Brighton's asking price down.
According to Bild, via GGFN, City have expressed their interest in signing Sosa, who is valued by Stuttgart between €20m (£17m) and €25m (£21.2m).
The report adds that both Barcelona and Bayern Munich are also closely monitoring the 24-year-old, with the latter looking to replace Omar Richards who has joined Nottingham Forest.
Sosa, who has previously attracted interest from London trio Arsenal, Chelsea and Tottenham Hotspur, has spent the last four years with Stuttgart after joining from Dinamo Zagreb in 2018.
The Croatia international struggled with injuries in his first two seasons with Die Roten, but he has since enjoyed two impressive Bundesliga campaigns as a left-back and left wing-back, providing 18 assists in 54 top-flight appearances.
It is thought that Stuttgart would be open to selling Sosa this summer if their valuation is met, even though he still has three years remaining on his contract with the German club.
Another left-back believed to be on City's radar is Hoffenheim's David Raum, who has also been linked with the likes of Bayern, Borussia Dortmund and Manchester United,.
However, the 24-year-old Germany international is valued at around €40m (£33.9m), roughly double the asking price of Sosa.
The likes of Arsenal's Kieran Tierney, Wolverhampton Wanderers' Rayan Ait-Nouri and Crystal Palace's Tyrick Mitchell have also been linked with at move to the Etihad Stadium this summer.
Guardiola has added three new players to his squad so far this summer in the form of Erling Braut Haaland, Kalvin Phillips and Stefan Ortega, while Julian Alvarez has joined up with the first-team squad after completing his move in January.
The Citizens are currently on their tour of the USA preparing for pre-season fixtures against Club America and Bayern Munich, before returning to England later this month to face Liverpool in the Community Shield.