Watson is not on a professional contract at West Ham United
It is claimed that Watson has impressed Roma manager Eusebio Di Francesco during a seven-day trial with the Serie A giants, and will remain there this week.
The 16-year-old has been a regular in West Ham's Under-18s this season, and won caps for England at Under-15 and -16 levels. The report adds, however, that the player is keen to play abroad.
West Ham are yet to tie Watson to a professional contract, but handed him a two-year scholarship deal earlier this year.
West Ham used to be renowned developers of young talent, with Rio Ferdinand, Frank Lampard, Michael Carrick and Joe Cole all going on to have successful careers after coming through at Upton Park.
However, the club has faced criticism for handing out fewer opportunities in recent years, with Declan Rice the only Hammrs player flying the academy flag this season.
Promising teenager Reece Oxford initially impressed at first team level, but has since found himself farmed out on loan with limited success.