The 17-year-old has made 12 first-team appearances for his current club, and a recent report claimed that City had held talks over a potential move for the attacker.
According to Romano, the Citizens are now closing in on the capture of the youngster, who could end up costing Pep Guardiola's side in the region of €19m (£17m).
"#MCFC close to complete the signing of Dario Sarmiento [17 years old] from Estudiantes. The 'real' fee will be €9m + add ons [potentially €19m]," the Italian journalist wrote on his official Twitter account.
Sarmiento, who scored four times in six appearances for Argentina's Under-16 side, largely operates as a right-sided attacker but can also play through the middle.
The South American made his professional debut at the age of 16.