The 27-year-old was an integral cog in Marco Silva's system during the 2022-23 season and contributed one goal and five assists from 31 Premier League matches, starting 29 of them.
Tete kept Arsenal loanee Cedric Soares out of the team during the second half of the campaign, as Fulham threatened a European charge before ultimately accepting a 10th-placed finish.
The former Lyon man has now registered three goals and eight assists from 80 games in a Fulham jersey since exiting France in the summer of 2020, but his contract situation is mired in uncertainty.
Tete is only tied down to the Cottagers until the end of next season, although Fulham do possess the option to extend his stay for another 12 months.
However, the Netherlands international's form is believed to have attracted the interest of Fulham's top-flight rivals, and The Sun reports that Liverpool are at the head of the queue.
Two other Premier League teams are also understood to be keeping a close eye on the situation, while an unidentified La Liga club have been credited with an interest too.
Given Tete's contract situation, Fulham could apparently be open to a sale for just £10.5m this summer as they look to avoid losing him on a free transfer in the summer of 2024.
Liverpool bolstered their full-back ranks in January with the capture of Scottish starlet Calvin Ramsay from Aberdeen, but the 19-year-old made just two appearances for the Reds in his debut season.
A serious knee injury and subsequent operation cut Ramsay's year short, but the teenager was already playing second fiddle to Trent Alexander-Arnold, who excelled in a hybrid role during the second half of the campaign.
The England international - who was heavily criticised throughout the season - scored one goal and set up seven more in Liverpool's final 10 Premier League matches, having been given license to roam the midfield during the Reds' attacks.
Despite his new role, Alexander-Arnold remains Jurgen Klopp's first-choice right-back, and James Milner would often provide backup to the 24-year-old when necessary.
However, Milner's exit on a free transfer has reduced Klopp's cover at right-back, while Naby Keita, Arthur, Roberto Firmino and Alex Oxlade-Chamberlain have also waved their goodbyes.
Defensive reinforcements could therefore be on the agenda for Liverpool, but the Reds are firstly expected to prioritise midfield additions, and they are supposedly confident of sealing a deal for Brighton & Hove Albion's Alexis Mac Allister next week.