Mina joined Barcelona from Palmeiras in January on a five-year deal with a release clause of €100m, but he has made only three La Liga appearances for the Spanish champions, getting his first assist for the club in Wednesday's win over Villarreal.
The Mirror reports that Barca manager Ernesto Valverde is happy to let Mina leave on loan so that he can get some game time, and become accustomed to European football.
Several Spanish clubs including Sevilla, Valencia, Villarreal and Celta Vigo have been linked with Mina, but Spanish television show El Chiringuito claims that Liverpool are in pole position to bring the Colombian to Anfield.
The signing would be a boost for Liverpool, who need defensive reinforcements if they are to challenge for major honours next year. Mina could partner Virgil van Dijk, who has greatly improved the Reds' defence since arriving in January.
Mina made his international debut for Colombia against Paraguay in June 2016 and has 10 caps for Los Cafeteros, scoring his first goal in a World Cup qualifier against Uruguay last year.
He is expected to be part of Jose Pekerman's squad for the 2018 World Cup as Colombia look to replicate their heroics from four years ago, when they reached the quarter finals.
Pekerman's team face Poland, Senegal and Japan in Group H.