The 19-year-old made his breakthrough into Marcelino's first team in the 2021-22 season, although he went 34 La Liga matches without recording a goal or assist.
However, Williams caught the eye with his performances in cup tournaments for Athletic, scoring two goals and setting up one more in four Copa del Rey outings as his side reached the semi-finals.
The teenager also struck the winning goal against Atletico Madrid in the semi-finals of the Supercopa de Espana before coming on at half time in the final defeat to Real Madrid.
Williams - who is the younger brother of fellow Athletic attacker Inaki Williams - is contracted to the Basque club for another two years after rising through their youth ranks.
Athletic's resolve could soon be tested, though, as Spanish outlet Fichajes claims that Man United and Liverpool are closely monitoring the Spaniard's progress in his homeland.
The report adds that Athletic could be open to a sale for the right price, but the La Liga club will still demand a hefty fee for the attacker given his contract situation.
Williams arrived at Athletic's academy from Osasuna in 2013 and registered nine goals and 12 assists in 26 games at youth level before making the step-up to the first team.
The 19-year-old has also earned five caps for Spain's Under-21 side, four of which came as substitute appearances in qualifying for the European Championships last year.
Man United are expected to entertain suitable offers for Anthony Martial this summer, but Marcus Rashford is seemingly set to stay despite previous speculation over his future.
However, five-time Ballon d'Or winner Cristiano Ronaldo has supposedly asked to leave the club as he does not feel that he can fulfil his remaining silverware ambitions at Old Trafford.
Club chiefs are determined not to let the 37-year-old go, though, and manager Erik ten Hag has stressed that Ronaldo is in his plans for the 2022-23 season.
Meanwhile, Liverpool have allowed Sadio Mane, Takumi Minamino and Divock Origi to leave the club this summer, with Fabio Carvalho and Darwin Nunez arriving to bolster the Anfield attacking ranks.
Mohamed Salah has also ended speculation over his future by signing a new three-year deal, but Roberto Firmino has now entered the final 12 months of his contract on Merseyside.
The Brazilian is expected to be offered an extension by the Reds, who are not being tipped to make any more signings this summer following the captures of Carvalho, Nunez and Calvin Ramsay.