The Spanish champions are understood to have accelerated their plans to bolster their defensive line following the performances of back-up duo Yerry Mina and Thomas Vermaelen during Sunday's 5-4 defeat to Levante - a result which ended their hopes of an unbeaten season.
Barca are in particular looking for a replacement for the 32-year-old Vermaelen, and Spanish outlet Sport claims that they are readying an approach for Lenglet as a result.
The 22-year-old is understood to have a €30m (£26.5m) buyout clause in his contract at Sevilla, which Barcelona are expected to trigger when the transfer window reopens.
Lenglet only joined Sevilla for €5m (£4.4m) last year, but he has quickly established himself as a first-team regular for the club.
The player could join compatriot Samuel Umtiti at Camp Nou, although Umtiti's own position at the club remains uncertain with talks over a new contract so far failing to reach a solution.