The 20-year-old has featured on 42 occasions for his MLS club in all competitions, scoring six times and registering one assist in the process.
Fall is familiar with Spanish football, though, having spent last season on loan at Villarreal, making 25 appearances for Villarreal B, scoring three times in the process.
The centre-back also featured on two occasions for the first team, appearing against Girona in La Liga on January 22, in addition to a Copa del Rey first-round clash with CD St. Amalia in November 2022.
According to The Athletic, Barcelona have come to an agreement with LAFC over a deal for Fall, who will move to Camp Nou on an initial loan deal.
The report claims that there will be a purchase option included in the agreement, with the Catalan outfit able to sign him permanently next summer for around €6.5m (£5.5m).
Villarreal were said to be in the driving seat for the youngster due to their relationship with him.
However, Barcelona have now come to an agreement with the MLS club and the player, with a deal expected to be announced before the deadline on Friday night.
Barcelona are said to be initially keen for Fall to play for their second team with a view to progressing to the senior side once he has fully settled at Camp Nou.
Fall was born in Senegal but moved to Orlando, Florida during his childhood before joining the Montverde Academy, where his performances led to him signing a two-year deal at LAFC.
Barcelona are widely expected to secure a loan deal for Manchester City defender Joao Cancelo before the end of the transfer window.
Meanwhile, a move for Atletico Madrid's Joao Felix remains a serious possibility, with Ansu Fati said to be on the verge of completing a loan move to Brighton & Hove Albion.
Amid the ongoing transfer speculation, Barcelona are currently preparing for their fourth La Liga game of the season, which will take place on Sunday evening against Osasuna.