The 22-year-old began his career in his native Argentina with Boca Juniors before joining Porto for €8m (£6.9m) last summer.
Varela, who primarily plays as a defensive midfielder, has since established himself as a first-team regular with the Portuguese giants, contributing with two goals and two assists in 30 appearances across all competitions.
As well as featuring 19 times in the Primeira Liga, Varela has started all seven of Porto's Champions League matches this term and was a standout performer in their narrow 1-0 first-leg win over Arsenal in last month's last-16 clash.
Varela has also caught the eye at international level with Javier Mascherano's Under-20s side and could be considered to represent the nation's Under-23s team at the 2024 Olympic Games.
Although Varela still has four-and-a-half years remaining on his Porto contract, the youngster has been linked with a number of top European clubs in recent weeks.
Indeed, a recent report claims that Liverpool are considering triggering the €70m (£60m) release clause in Varela's contract.
However, Portuguese news outlet Maisfutebol states that Man City also hold an interest in the midfielder and have been following his performances 'very closely' for some time.
The Citizens are said to have closely monitored Varela's progress during his time at former club Boca Juniors and have since attended recent Porto matches to scout the youngster.
It is understood that Man City are yet to enter negotiations for Varela, who has also been linked with Paris Saint-Germain and Borussia Dortmund, but a 'profile evaluation process' of the player is underway.
Man City are expected to delve into the summer transfer market for a new midfielder if they decide to part ways with Kalvin Phillips, who is currently on loan at West Ham United.
The future of key playmaker Bernardo Silva is also believed to be uncertain, considering the Portuguese has on numerous occasions expressed his desire to pursue a fresh challenge away from the Etihad Stadium.
Midfield fulcrum Rodri is one of the first names on the teamsheet for Man City along with Kevin De Bruyne, when fit, while Bernardo, Mateo Kovacic and Matheus Nunes - the latter two both signed by the Citizens last summer - are other midfield options at Pep Guardiola's disposal.
Defensive trio John Stones, Manuel Akanji and Rico Lewis have also been deployed in deep-lying midfield roles by Guardiola this season.
Varela is not the only midfielder that has been linked with a move to the Etihad, as a recent report claims that Man City are ahead of Liverpool and Barcelona in the race to sign Bayern Munich's Joshua Kimmich.