The 23-year-old has been in impressive form this season, attracting interest from the Premier League duo heading into the summer.
However, Reds boss Jurgen Klopp has now emerged as favourite to sign the winger, with club chiefs said to have already met with his agent Jorge Mendes, who owns 50% of his rights, to discuss a deal.
Both English clubs are keen to reinforce their ranks during the upcoming transfer window as they look to mount a top four challenge next season.
Silva featured 49 times in all competitions for his side this term, so far scoring 12 goals while providing another eight assists in the process.
The Braga ace has been included in Portugal’s plans for EURO 2016 and could see his value and status skyrocket over the coming months should he impress in France.