Even though the Catalan club have been struggling financially this year, they remain in the market for new additions if they are able to balance their books.
Barca only recruited free agents this summer - including City pair Sergio Aguero and Eric Garcia, who saw their contracts expire - however Sport reports that the La Liga giants also made a swoop for Torres, which was quickly rebuffed by Pep Guardiola's side.
Torres, who joined City from Valencia in the summer of 2020, is now considered a first-team regular under Guardiola after the Citizens failed to sign a centre-forward.
The 21-year-old enjoyed his maiden campaign at the Etihad Stadium last season, scoring 13 goals and providing three assists across all competitions, as well as winning the Premier League title and the EFL Cup.
Barcelona are also understood to have a strong interest in Man City winger Raheem Sterling, with one report suggesting they are prepared to make a loan move for the England international in January.