El Confidencial says Firpo's rapid progress has come to the attention of City manager Pep Guardiola, who has had scouts posted to watch him in the opening weeks of the season.
The 21-year-old can also play in central defence as well as on the left flank.
The defender was a star performer for Quique Setien's team in the second-half of last season.
Along with City, Firpo is also on the radar of Arsenal, which considered a serious move for the youngster over the summer.
The midfielder extended his contract last month to 2023, with a buyout clause of €60m.