The Catalan giants are expected to enter the loan market in January, due to their financial troubles, with Sterling believed to be one of their primary targets.
Man City remain hopeful that the 26-year-old will sign a new long-term contract and they are unwilling to see the forward leave unless his €75m (£63.7m) valuation is met, a figure that Barca cannot afford.
Barcelona's inability to spend big on transfers means they could initiate a potential swap deal for the England international, something which they attempted last summer involving Ousmane Dembele, according to El Nacional, before the Frenchman picked up an injury which prevented any deal from materialising.
The same report claims that City would also be interested in a potential player-exchange deal involving Sterling, but only if 2021 Golden Boy winner Pedri were to move in the opposite direction.
Pep Guardiola is believed to be a huge admirer of the 18-year-old midfielder and the Spanish head coach would be open to Sterling's departure to Camp Nou if Barca's teenage starlet were to arrive at the Etihad Stadium as his replacement.