Musah starred for the USA as their young side exited the tournament at the round of 16, losing 3-1 to Netherlands.
According to Italian media outlet Calciomercato, the three English clubs interested in signing the player include Arsenal, Chelsea and Liverpool.
In addition, Serie A side Inter Milan are also listed in the report as being one of the interested parties.
The 20-year-old made his debut for Valencia in 2020 following a year in their youth set-up, and has totalled 81 appearances so far.
Musah also made his national team debut not long after joining the club and has since gone on to earn 22 caps for his country.
Despite his American allegiance, he came through the Arsenal youth system from 2012 to 2019 and also featured at England youth level from Under-15 to Under-18 before switching nationality to the USA.