The Brazil star signed a new five-year contract at Anfield as recently as January.
However, Barcelona's long-term admiration may finally lead to a transfer this summer.
According to Spanish newspaper Sport, conversations with Liverpool have already reached an advanced stage.
Philippe Coutinho has nine goals and six assists in 25 Premier League appearances for Liverpool
Coutinho's style and profile are key factors behind Barca's desire
It is said only a final step is left to take over a move, despite the Reds' denial.
Philippe Coutinho's style and profile are key factors behind Barca's desire to sign the 24-year-old.
And the Liverpool playmaker is among a host of players on the agenda for this summer at the Nou Camp.
Sport add there are nine or 10 names who have already been contacted ahead of the end of the season.
On their shortlist, Arsenal ace and former Barca youth Hector Bellerin is deemed a more necessary option.
Luis Enrique has been short of real options in his role and Bellerin is a target.
Meanwhile, Barca also dream of landing the likes of Paris Saint-Germain midfielder Marco Verratti and Juventus forward Paulo Dybala, although the latter did put pen to paper on a new contract yesterday.
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Hector Bellerin is also wanted by Barcelona, despite his poor form at Arsenal in 2017 Barcelona transfer odds: Which Premier League stars could head to La Liga? Wed, March 29, 2017
Which Premier League players are most likely to join Barcelona in the summer, according to odds provided by 888sport?
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Which Premier League players are most likely to join Barcelona this summer?
Despite the array of players contacted by Barca, their plan is to invest in quality not quantity.
Last summer's failings in the transfer market means top talents are required to properly support the squad.
Tuesday's 3-0 defeat to Juventus in the Champions League quarter-final first leg highlighted Barca's problems, with no manager appointed yet either for next term.