The United States international has been a regular for his Catalan side this season despite some injury problems, making 31 appearances in all competitions, contributing three assists in the process.
Dest still has more than three years left to run on his contract at Camp Nou, having penned a five-year deal with Barcelona upon his arrival from Ajax in October 2020.
However, there has been speculation surrounding the right-back's future this year, and according to Marca, Xavi's side would be prepared to sell him for €25m (£21.1m) this summer.
The report claims that Sergi Roberto and Dani Alves are both set to sign new deals at Barcelona, while the expected arrival of Cesar Azpilicueta from Chelsea means that Dest could be surplus to requirements.
The 21-year-old has made 72 appearances for Barcelona in all competitions, contributing three goals and four assists in the process.
This term, he has featured on 21 occasions in La Liga, in addition to playing a further 10 times in the Europa League, Champions League and Copa del Rey.
The American has been on the sidelines since the end of April with a muscular problem, though, and the issue is also expected to rule him out of Barcelona's final game of the season against Villarreal this weekend.
Man United have recently been credited with an interest in Dest, and the reported €25m (£21.1m) price could prove to be attractive to the 20-time English champions, who will seemingly be in the market for a new right-back during this summer's transfer window.
Incoming Red Devils head coach Erik ten Hag has reportedly made Aaron Wan-Bissaka available for transfer during the summer market.
The 24-year-old has made 26 appearances in all competitions this term but has fallen behind Diogo Dalot in the pecking order for the right-back spot since Ralf Rangnick's arrival as interim head coach last December.
Wan-Bissaka could allegedly leave on loan this summer, but Ten Hag is believed to be keen to keep hold of Dalot for the 2022-23 campaign, with the Portugal international playing a lot of football in the second half of this season.
The former Porto youngster has made 29 appearances this term, including 23 outings in the Premier League, but he only has little over 12 months left to run on his contract at Old Trafford, so a new deal could be signed in the near future.
Man United will be bidding to secure a spot in next season's Europa League when they travel to Crystal Palace on the final matchday of the 2021-22 Premier League campaign.