The goalkeeper joined the Danish club on loan from Barcelona with an option to buy for €1.5m and has established himself as a regular starter.
Kochen has never made a competitive first-team appearance for Barcelona despite being called into the senior squad almost 100 times. He still hopes that opportunity can eventually arrive at the Spotify Camp Nou.
“Obviously, I have my long-term goals,” Kochen told Goal. “Right now I am on loan at Lyngby, I want to compete at the highest level and give everything for that club. At the same time, I come from Barcelona, so being able to go back? It would be every kid's dream: to return to such a big club and have the opportunity there. That is another one of my goals.”
The American also reflected on the competition he experienced from a young age after joining Barcelona's system.
“You have to fight for a position from a very young age and learn the values of competition from an early age,” he said. “That was what surprised me the most, I would say, about everything.”
Kochen also recalled the experience of being around Barcelona's first-team stars, including Lamine Yamal, Pedri and Raphinha.
He described seeing supporters celebrate the club's trophies through the streets of Barcelona as “incredible”, remembering the scenes as “a madness to see the whole city outside”.
The goalkeeper also paid tribute to former Barcelona teammates Wojciech Szczesny and Marc-André ter Stegen, while naming Manuel Neuer and David de Gea among other goalkeepers he admires.
Kochen's immediate focus remains on Lyngby and making the most of his first regular senior football. The loan has given him the opportunity to play consistently and has now been followed by his senior international debut for the United States.
That experience could ultimately strengthen his prospects of returning to Barcelona, although the €1.5m purchase option means Lyngby could have a route to make the move permanent.
For Kochen, however, the ambition remains straightforward: establish himself through regular football before seeing whether the dream of returning to Barcelona can become reality.