After working his way through Barca's famed La Masia academy, Fati made his debut for the senior team at the age of just 16 in 2019.
Last season the Spaniard managed just seven appearances in La Liga after suffering a serious knee injury, but he has recently returned to training after 10 months on the sidelines.
Mendes had been hoping to push forward a significant salary increase in a contract renewal prior to his return to the first team, in case his client struggled to recapture his previous form.
Catalan newspaper outlet El Nacional reports that the product of La Masia has been placed in the shop window by the super-agent Mendes, as he looks to scare the Spanish giants into increasing their contract offer to his client.
The report goes on to claim that Manchester City are one of the sides to have been contacted, but manager Pep Guardiola has refused to sanction the deal due to his strong relations to Barca, especially returning president Joan Laporta.
Fati has made 41 appearances for the Barcelona first team in total, scoring 13 goals.