The France international has entered the final 12 months of his deal with the Catalan giants, and little progress has been made with regards to an extension.
As a result, Liverpool sporting director Michael Edwards is rumoured to be putting the framework together for an approach in January, with the Reds potentially starting to look ahead to life without Sadio Mane and Mohamed Salah.
Here, using statistics from the 2020-21 domestic season, Sports Mole looks at how the trio compare ahead of Dembele's possible switch to Anfield.
Dembele is yet to establish himself as a consistent goalscoring maestro at Barcelona - helped in no small part by a plethora of injury woes - as the Frenchman chalked up six goals from 30 league appearances last term - 19 of them starts.
Meanwhile, Salah ended yet another prolific Premier League campaign with 22 strikes to his name last season, while Mane - who did not enjoy the best of seasons by his own admission - chalked up 11 goals in the top flight.
While Dembele does not rank higher than his counterparts on many statistical categories, he was dispossessed the fewest number of times per game on average - 1 compared to Salah's 2.2 and Mane's 1.7 - while 1.7 instances of bad control per game is also the best out of the trio.
However, the Barcelona man only averaged 1.8 shots per game compared to Salah's 3.4 and Mane's 2.7, but the fact that he played over 1,000 fewer minutes of domestic football last season must be taken into account.
None of these three players is renowned for their contributions in their own defensive third, but Mane stands out above the other two statistically, with Dembele and Salah both averaging 0.5 tackles per game last term.
In contrast, Mane racked up an average of 1.4 tackles per 90 in league action, but the Senegalese superstar also committed 1.5 fouls per game, with Dembele's 0.5 the fewest in that respect.
Salah and Mane would also end the season with an average of 0.3 clearances per game - while Dembele did not make a single clearance in league action last season - and Salah was dribbled past on the fewest number of occasions.
Unsurprisingly, the trio did not chalk up one red card between them in the Premier League or La Liga last season, as Mane picked up three bookings, Dembele two, while Salah was not cautioned once.
Dembele's 30 appearances in La Liga last season saw him chalk up a mere three assists for his teammates, while Salah registered five and Mane led the way with seven, as well as making the most key passes per game with 1.7.
To put these statistics into perspective, Salah has already banked six goals and three assists in seven league appearances this season, which is exactly what Dembele registered in 30 games for the Blaugrana last term.
However, the Barcelona man would rank highest in pass completion last season, as 85.8% of his passes in La Liga were accurate compared to 83.7% for Salah and 78.7% for Mane in the Premier League.
Dembele would previously register 13 assists in 32 Bundesliga appearances during his farewell season with Borussia Dortmund - with his talent evident if yet unfulfilled - and Liverpool could do far worse pieces of business than take a punt on a World Cup winner without giving Barcelona a penny, but the last thing that Jurgen Klopp needs is more long-term injuries to work around.