The United States international returned to Camp Nou earlier this summer following a loan spell at AC Milan, but he is not in the plans of the Catalan outfit's head coach Xavi.
Dest's future has been the subject of much speculation in recent weeks, with a number of clubs believed to have expressed an interest in his signature.
According to Marca, Nice are set to sign Dest on loan for the 2023-24 campaign, although the details of the agreement still need to be addressed, as the French outfit are not prepared to pay his full salary.
PSV Eindhoven have also been credited with an interest, but it is believed that the American is against returning to the Dutch league, having previously represented Ajax.
The 22-year-old has been with Barcelona since 2020, making 72 appearances, including 41 in all competitions during a successful first season at the club.
Meanwhile, Everton are allegedly in discussions with Southampton over a deal for Che Adams.
The Scotland international has been heavily linked with a move away from the Saints this summer, with a number of clubs believed to be keen to bring him back to the Premier League.
According to BBC Sport, Everton are currently in talks over a £12m deal for the striker.
The report claims that the Toffees are determined to bring another attacker to the club before the end of the transfer window and have identified Adams as their leading target.
The 27-year-old made the move to Southampton from Birmingham City in 2019, and he has represented the club on 148 occasions in all competitions, scoring 33 times in the process.
Adams has found the back of the net on 25 occasions in the Premier League, while he has two goals in two Championship appearances at the start of this season.
Elsewhere, Leeds United are reportedly weighing up a move for Norwich City forward Josh Sargent.
The 23-year-old made the move to Norwich from Werder Bremen in 2021, and he has represented the Canaries on 72 occasions, finding the back of the net 18 times.
Sargent has scored once in two Championship appearances this season, while he netted 13 times in the second tier of English football during the 2022-23 campaign.
According to Football Insider, Leeds are considering making an attempt to sign the United States international before the end of the summer transfer window.
The report claims that former Norwich boss Daniel Farke, who is now in charge of Leeds, is driving the club's interest in the attacker.
Sargent scored 15 times for Werder Bremen ahead of his move to English football, while he managed two Premier League goals during his first season at Carrow Road.