Throughout the recent transfer window, Sterling was allegedly one of a number of City players who would have been allowed to leave the Etihad Stadium for the right price.
An offer meeting City's valuation never materialised and Sterling has since gone on to make three starts and four substitute appearances in all competitions.
However, according to Sport, the Premier League champions were prepared to part ways with the 26-year-old if it meant being able to sign Fati.
Given their financial problems, the report suggests that Barcelona would have only been prepared to sell Fati if they received a straight-cash offer which proved too good to turn down.
The 18-year-old, who has been sidelined with a long-term knee injury, is in contention to return to the Barcelona squad against Levante on Sunday. body check tags ::