The playmaker is currently on loan at Porto and has attracted interest from the Premier League as his time at the Nou Camp appears to be coming to an end.
Spanish newspaper Fichajes claims that Klopp is a big fan of Tello and has sought out meetings with the Liverpool board to make the move possible when the transfer window opens in January.
Klopp's chances of landing Tello were boosted when former Barca president Joan Laporta admitted that the club may be forced to sell off some its younger players in order to rectify their financial problems.
Laporta said: "The situation isn't good and to balance the accounts Bartomeu will have to sell players or other assets. The best solution is to sell big players. They say Manchester United have been interested in Neymar but that's a result of the current mismanagement."