https://www.mundodeportivo.com/futbol/fc-barcelona/20211003/1001695695/dani-olmo-sterling-opciones-reforzar-delantera-invierno.html
Considering the market value of Sterling and his wage amount, I highly doubt that Barcelona can afford him right now. Maybe after a season or two, but right now the deal seems unlikely to happen. Although this season he has had a slow start but last season he got 10 goals and 7 assists in 31 games for City, not to mention the chances he created every match. Sterling is still an important piece for City and they should not let go of him for a small fee.