The United States international moved to PSV on loan last summer, and he has been in impressive form for the Dutch outfit during the 2023-24 campaign, making 37 appearances in all competitions, contributing two goals and seven assists in the process.
The Eredivisie team are believed to have the option to sign the right-back permanently during the summer market for a fee in the region of €10m (£8.6m).
Dest has said that PSV are "very satisfied" with his performances, and he has opened the door to make the move to the club on a long-term basis during the summer market.
Dest confirms talks over permanent PSV move
When questioned by ESPN on his future, Dest said that "there is certainly a possibility" he could make the move to the Dutch outfit on a permanent basis.
"PSV is very satisfied with me and I am enjoying myself here. We are doing well as a team, we are close to being champions and next year we will play in the Champions League again," he added.
"Everything has to be right and it's up to us to fix everything to reach a good agreement."
Dest has played 25 times in the Eredivisie this season, scoring twice and registering six assists, with PSV sitting at the top of the table, nine points ahead of second-placed Feyenoord.
The defender represented AC Milan on loan during the 2022-23 campaign, but he only featured 14 times for the Italian giants before heading back to his parent club.
Dest does not appear to have a future at Barcelona
Dest's performances for Ajax led to Barcelona bringing him to Camp Nou in October 2020, and he was an important player for the Catalan outfit in his first season at the club.
Indeed, the right-back played 41 times in 2020-21, including 30 outings in La Liga, and he also featured on 31 occasions during the 2021-22 campaign, but he was then sent on loan to Milan in the summer of 2022.
Barcelona head coach Xavi could not find a spot in his squad for Dest for the current season, but there will be a change of manager at the club this summer.
Even so, there is unlikely to be a change to Dest's situation, with the 23-year-old needing to leave Barcelona on a permanent basis for the sake of his career, and a switch to PSV is seemingly on the cards.