Mina joined Barcelona from Brazilian outfit Palmeiras in January but has managed just five appearances for the La La champions.
The Colombia international now looks set to leave the Nou Camp on loan next season to further his development.
And according to Spanish TV programme El Chiringuito, Liverpool have struck a deal with Barca to take the 23-year-old for the 2018/19 campaign.
Jurgen Klopp has five centre-backs on the books at Liverpool but he is yet to decide on his preferred partner for £75m January signing Virgil van Dijk.
La Liga clubs Sevilla, Valencia, Villarreal and Celta Vigo are also said to be interested in loaning the young defender.
Mina, who cost £11m five months ago, has struggled to displace Barcelona’s preferred centre-back partnership of Gerard Pique and Samuel Umtiti.
Barca boss Ernesto Valverde recently said of his lack of game time: "Yerry Mina? I have four centre-backs and I usually name three on the [matchday] list.
"Those who have been playing are Gerard Pique and Samuel Umtiti, and when Thomas Vermaelen's played, he's done well."
Mina is contracted at the Nou Camp until the summer of 2023 and is said to have an £88m release clause in his contract.