Monaco also sounded out a move for Dest, but all four clubs were knocked back by both the player and Barca. Therefore, an official offer never arrived and numbers were never even discussed.
Sources explain the clubs had hoped to take advantage of Barca's financial situation by making a move for Dest, who joined the Catalan club from Ajax for an initial €20 million last September.
Barca need to raise funds and reduce the wage bill to be able to register their new signings and Lionel Messi's new contract while complying with LaLiga's financial fair play rules. President Joan Laporta has said the club are open to "all proposals."
Barca are well-stocked at right-back. In addition to Dest, they also have Emerson Royal and Sergi Roberto, while Oscar Mingueza can also play there, but they are not planning to move the USMNT defender on. Coach Ronald Koeman is especially keen to keep Dest, 20, who has no intention of leaving.
One source with knowledge of the situation said Barca were satisfied with Dest's first season at the club and believe in his potential to establish himself as the club's No. 1 right-back moving forward while also providing backup for Jordi Alba at left-back.
He made 41 appearances in his first season at the club, scoring three goals, and has started both of their friendlies in preseason so far. He is with the squad in Germany ahead of Saturday's match against Stuttgart.
Meanwhile, Barcelona remain in "constant talks" with youngster Ilaix Moriba's representatives over a new contract, sources have told ESPN.
Barca met with Ilaix's camp in person on Wednesday and remain in continual contact via the telephone but they are no closer to reaching an agreement over a fresh deal.
The midfielder, 18, is out of contract next summer and has been pushed to the sideline as negotiations continue. He is training with the B team but is not featuring in friendlies. He's been left out of the squad for Thursday's game against FE Grama.
A source said Barca fear his agents are keen to run down the current terms before leaving for free in 2022, when they would be able to pocket a substantial signing-on fee elsewhere.
Despite that, the Blaugrana continue to push for a three-year deal, which would allow both parties to review the situation in 2024, when Ilaix would still only be 21.
After breaking into the first team in January, Ilaix went on to make 18 appearances for Koeman's side last season. He scored one goal.