The England international has been with the Citizens since July 2015, making 307 appearances in all competitions, including 15 outings during the 2021-22 campaign.
The 26-year-old has only managed two goals and two assists for the English champions this term, though, and he was an unused substitute in the Manchester derby against Manchester United on Saturday.
According to Mundo Deportivo, the Englishman 'wants to leave' Pep Guardiola's side in January, but the Citizens 'would not make it easy' for him to seek pastures new.
The report claims that Barcelona are keen to agree a loan deal with the Premier League champions, which would include the option of a permanent deal next summer.
Sterling was on the scoresheet in Man City's 4-1 win over Club Brugge in the Champions League last week. body check tags ::