International career
Due to his parents' nationality, Vassilev was eligible to represent both the United States and Bulgaria at international level. He represented the United States at the 2017 FIFA Under-17 World Cup in which he played 4 of 5 games as the team reached the quarterfinals. He also made appearances for the United States men's national U16, U18 and U20 soccer teams.
At the beginning of 2020, Georgi Dermendzhiev, the Bulgaria national team head coach, stated that Vassilev had politely declined a call up for the Bulgaria under-21 team to continue representing the United States. In May 2023, the new Bulgaria national coach, Mladen Krstajić, reached out to Vassilev regarding a potential call-up, but was informed that the player would want to focus on his adaptation to his new club and would discuss a call-up for the next matches.
On October 8, 2023, Vassilev was called up to the United States under-23 national team ahead of friendlies against Mexico and Japan, playing in the 4–1 win over Japan.
On January 18, 2025, Vassilev made his senior national team debut in a 3–1 win over Venezuela. On January 22, 2025, he made his first senior team start in a 3–0 win over Costa Rica.