Williams is regarded as one of the best young prospects in the country and his stock has risen after making his Wales debut in midweek against Holland.
The 18-year-old impressed off the bench in the international friendly and his performance has alerted several Premier League sides to his potential.
Williams is entering the final year of his contract at Fulham and his suitors are actively monitoring his situation at Craven Cottage.
Fulham are determined to keep Williams and they are keen to tie him down to a new long-term deal to ward off interest this summer.
Williams became the youngest-ever scorer in the FA Cup proper after scoring for MK Dons as a 16-year-old and his emergence at MK Dons saw Fulham sign him in the summer of 2012.