Moreno, 27, has featured just five times under manager Jurgen Klopp this season as his erratic form saw him lose his place in the team to Andy Robertson since last season.
However, a report in Spanish publication Sport claims Barca want to sign the error-prone defender as back-up to compatriot Jordi Alba.
It was previously reported that the Spain international was signed from Sevilla in 2014 for £12million was set to join Italian side Lazio - but the new interest from the Blaugrana has now swayed his mind, the report added.
The left-back is said to be in talks over a two-year contract which will be finalised once his current deal expires with the Reds at the end of the season.
Since joining the club, Moreno has featured 141 times, scoring three goals, while registering 11 assists.
He has featured in just five games under Jurgen Klopp this season.