While the 21-year-old has featured heavily for the club this season, he has apparently lost the trust of manager Xavi.
It could ultimately be a disappointing end for the United States defender, having come in with high hopes after signing from Ajax in October 2020 for €25million (around £21.5m).
Under former manager Ronald Koeman, Dest featured heavily for the La Liga giants but could now be departing the club after El Nacional also reported that Xavi prefers Sergi Roberto, Ronald Araujo and Oscar Mingueza.
Dest was subbed off at half-time as Barcelona lost 3-0 to Bayern on Wednesday night, exiting the Champions League at the group stage for the first time in 21 years.
And it has been reported Dest wants to move to the Bundesliga champions and has asked Barca president Joan Laporta to sell him.
Significantly, Bayern Munich may also be interested in securing Dest's services, having already attempted to sign him when he was at Ajax.
The 21-year-old has featured in 15 games this season starting 12 of them and Dest has been utilised in a number of positions, showcasing his versatility.
Furthermore, given that Barca are still in a financial crisis, extra funds would certainly be welcomed as they look to fix all the issues that were caused under former president, Josep Maria Bartomeu.