Manager Jurgen Klopp has recently insisted that he does not envisage Liverpool making any further signings during the summer transfer window.
However, Journal de Noticias claims that the Premier League giants have become the latest club to register an interest in Portugal international Nunes.
The 23-year-old has already been linked with Chelsea and Wolverhampton Wanderers over the coming weeks with the player having a £50.6m release clause in his contract.
The report says that last season's Champions League runners-up have been in 'direct contact' with their counterparts at the Primeira Liga outfit.
Nunes has made a total of 99 appearances for Sporting in all competitions, contributing seven goals and eight assists.
Meanwhile, Tottenham Hotspur are said to be contemplating whether to try to secure a reunion with full-back Kyle Walker-Peters.
At the age of 23, the Englishman had only made 24 appearances for the North London outfit, subsequently resulting in a loan switch to Southampton which was eventually made permanent.
Since then, Walker-Peters has become a mainstay on the right-hand side of the defence, as well as earning recognition on the international stage with England.
According to CBS reporter Ben Jacobs, Spurs are open to handing the player a second spell at his former club as they consider their options at right wing-back.
As it stands, Middlesbrough's Djed Spence appears the clear favourite to be signed under Antonio Conte, but Walker-Peters is regarded as a realistic alternative.
Like many other players in his position, Jesse Lingard remains without a club after his release from Manchester United, but the midfielder is not short of opportunities.
Having endured a frustrating final 12 months at Old Trafford, the 29-year-old is currently deliberating over where to spend the next phase of his career.
According to the Daily Mail, a final decision will be made over the coming days with the England international having options on several different continents.
The report claims that Premier League, MLS and Saudi Arabian teams are all in the running for the playmaker, the latter being a £10m-per-year offer from Al-Shabab.
Lingard would allegedly prefer to sign for an English club with West Ham United and Everton having been linked with his signature in the past.
Aston Villa are seemingly on the verge of being backed into a corner regarding the future of Carney Chukwuemeka, who has less than 12 months remaining on his contract.
While the West Midlands outfit are desperate for the youngster to pen fresh terms, the midfielder is receiving interest from clubs in the Premier League and abroad.
With the situation seemingly far from being resolved, Villa boss Steven Gerrard has left the England Under-19 international out of the club's pre-season tour.
Nevertheless, according to talkSPORT, Villa still intend to demand in the region of £20m for Chukwuemeka if he continues to reject a new deal.
Manchester City, Man United, Barcelona and Borussia Dortmund are all said to be monitoring the situation.