Klopp is believed to be a huge fan of the Frenchman, with 'Mundo Deportivo' claiming that the 'Reds' attempted to lure the youngster to Anfield before his mega-money move to Barcelona in 2017.
The Spanish champions paid Borussia Dortmund a whopping £134m for his services barely 18 months ago, but whilst the 21-year-old has won the World Cup with his country during that time, his displays at club level have largely flattered to deceive.
Having been signed to replace Neymar following his move to PSG, the pressure was always going to be on Dembele to deliver fireworks straight off the bat at Camp Nou, only for injuries to prevent slow his progress in his first season at the club.
That he has only managed to play the full 90 minutes on two occasions in 16 games so far this season has led many to conclude that he is not fully trusted by Ernesto Valverde, though his statistics show a healthy return of six goals from 14 games in all competitions.
First-team fixture of not, Dembele remains one of the brightest young prospects in world football and Liverpool seemingly head the queue for his signature should Barca decide to cut their losses.