The Reds are currently searching for Jurgen Klopp's replacement after the German revealed in January that he would leave the club at the end of the season.
A recent report claimed Ruben Amorim had reached a verbal agreement to become Liverpool's new manager, before the Sporting Lisbon boss strongly denied those rumours.
While Amorim remains the frontrunner to replace Klopp, Liverpool are also scouting the Portuguese top-flight for potential additions to their playing squad.
According to O Jogo, Liverpool representatives were sent to watch Varela in Porto's recent league game against Vitoria de Guimaraes.
The Argentine started Sunday's 2-1 defeat at Estadio do Dragao, before he was replaced by Ivan Jaime in the 56th minute.
Although he played less than an hour at the weekend, Varela is regarded as a key player in Sergio Conceicao's side, having made 36 competitive appearances since arriving from Boca Juniors last summer.
In addition to Liverpool, the 22-year-old is attracting interest from Chelsea, Manchester City, Manchester United, Bayern Munich and Atletico Madrid.
Varela supposedly has a €70m (£60m) release clause in his Porto contract which is set to run until the summer of 2028.
Do Liverpool need a new midfielder?
On the surface, Liverpool appears to be well-stocked in the engine room after recruiting Wataru Endo, Alexis Mac Allister, Ryan Gravenberch and Dominik Szoboszlai.
However, they still seem keen to bring in a defensive midfielder to play a holding role and offer greater protection to their backline.
Liverpool are also expected to lose at least one option in the middle of the park, with Thiago Alcantara set to leave at the end of the season.
Thiago will be allowed on a free transfer when his contract expires this summer, having been restricted to just five minutes of playing time this season due to injury.