The Reds are not the only ones monitoring the 23-year-old, though, with several English clubs having scouts in attendance at Thursday's Europa League clash with Tottenham Hotspur.
Rodrigo started that game on the bench, but representatives from Manchester United, Chelsea and West Bromwich Albion were offered a 15-minute cameo in which to pass judgement on the Spanish striker.
Benfica coach Jorge Jesus is not surprised to find the former Real Madrid trainee falling under the spotlight, and has confirmed that Liverpool are among those leading the chase for a much sought-after signature.
Asked specifically about the interest from Anfield, he said: "It's normal. Every Benfica player is in a big window.
"The league is full of high quality players so it's normal for other clubs to be interested.
"Rodrigo is going through a good moment."
Rodrigo has graced the Premier League in the past, taking in an uneventful loan spell at Bolton Wanderers when just 17 years of age, but he has improved his game considerably since mustering just one goal in 17 appearances for the Trotters.
A man who has netted 10 times in his last 16 outings this term could soon be on his way back to the English top flight, but his father and agent Adalberto Machado insists no thought will be given to future plans until the end of the current campaign.
Ahead of Benfica's 2-2 draw with Spurs which carried them through to the quarter-finals of the Europa League, Machado told TMW: "I expect to meet the club at the end of the season.
"We want the best for the player and for the club, but at the moment Rodrigo is only concentrating on Benfica and winning titles at the end of the season."