According to Sky Sports, La Blaugrana are keen on acquiring the services of the Belgian as back up to number one stopper Marc-Andre ter Stegen ahead of the new La Liga season, beginning on August 17.
With the 30-year-old having fallen down the pecking order behind Loris Karius at Anfield and now with the arrival of world-record signing Alisson from AS Roma, the move would nevertheless come as something of surprise move for the depending Spanish league champions.
Mignolet's agent has claimed there are several offers for his client while Besiktas were reported to have thrown their hat into the ring. However, it is understood the Turkish side have yet to make a firm approach, with sources now suggesting Barcelona could make a move.
Since making the switch from Sunderland in 2013, Mignolet has failed to win over his critics on Merseyside during the course of four seasons.
Since Jurgen Klopp's arrival, Mignolet has been rotated with Karius, while the German was preferred for the majority of the 2017/18 season. Alisson's arrival at Anfield has made Mignolet's position largely untenable with the former Sunderland man not content to play third fiddle.
While Ter Stegen is the firm number one choice for Ernesto Valverde at the Nou Camp, the German's deputy Jasper Cillessen is expected to leave Catalonia this summer to seek first team opportunities. That could open the door for Mignolet to make the switch to Iberia, but his chances of first-team action would likely be as restricted if a move should be completed.