Moreno - who is out of contract at Anfield in the summer - was widely expected to pen a deal with Serie A side Lazio having been seen in Rome last week, when he was pictured with former Reds teammate and current Lazio midfielder Lucas Leiva.
But it is now claimed that Barca have moved ahead in the battle for his signature on a free transfer, and will snap him up as cover for the club's current left-back Jordi Alba.
Moreno, 26, signed for the Reds from Sevilla for £12m in the summer of 2014, but he has had an up-and-down time of it at Anfield.
Although occasionally impressive, lapses in concentration such as in the 2016 Europa League final against his previous employers often used to count against him.
He did earn his place back at the start of last season and impressed, but injuries and the emergence of Andy Robertson has made game-time extremely limited for him.
He has featured just five times in all competitions this season, with his last game coming in the FA Cup loss at Wolves in January.
Sport claim that Moreno is one of three players Barca are moving closer to signing, along with Ajax defender Matthijs de Ligt and Eintracht Frankfurt striker Luka Jovic.