The Spaniard has not been at his best since arriving at Anfield.
It comes as Adriano, the Spanish champion’s resident Jordi Alba replacement, gets set to leave the club this summer.
Barcelona reportedly have Moreno on a shortlist along with Ricardo Rodriguez of VfL Wolfsburg, Layvin Kurzawa of AS Monaco and Tottenham Hotspur’s versatile Jan Vertonghen.
The club have youngster Grimaldo coming through the ranks but it is believed Luis Enrique is unsure of his ability to shine in the first-team at the Nou Camp.
Moreno has only been at Liverpool for one season. The Reds signed him from Sevilla last summer, in a deal reported by the BBC to be worth £12 million from Sevilla last August.
However, despite high hopes, his first season at Liverpool was questionable in terms of its success.
He showed flashes of brilliance but overall struggled to settle, which could be expected in a first year in a new country.
It was his lack of defensive abilities, however, which had most people concerned about his future at the club.
Barca would not be able to make a move for the player until January at the earliest but they are believed to be using their current transfer embargo period to get their house in order early for 2016.