The 21-year-old is regarded as an integral part of the Athletic side, having scored six goals and provided 11 assists in 27 competitive appearances this season.
Williams scored the latest one of those six goals in the 3-0 win over Atletico Madrid in the semi-final second leg of the Copa del Rey.
While he is hoping to guide Athletic to silverware alongside his brother Inaki Williams, the youngster could be on the move in the summer amid interest from the Premier League.
Arsenal were previously said to be in pole position for Williams' services, while a recent report suggested Chelsea were also among his admirers.
According to The Mirror, Tottenham could now join their London rivals in the race to secure Williams' signature ahead of the 2024-25 campaign.
The Spain international signed a new deal in December to extend his contract with the Basque side until the summer of 2026.
However, he continues to be linked with a move away from San Mames, with his contract said to include a €50m (£43m) release clause.
Spurs are seemingly keen to strengthen their attacking options, especially with uncertainty surrounding the future of Bryan Gil and Timo Werner.
Gil has found playing time hard to come by and could be moved on in the summer, while it remains to be seen whether Spurs will pursue a permanent deal for Werner, who is currently on loan from RB Leipzig.
Aston Villa are also believed to be showing a keen interest in Williams after Unai Emery reportedly held talks with Williams in a private hotel last June.
Although the Williams opted to stay put for the 2023-24 campaign, the Villans could renew their pursuit in the upcoming summer window.
Real Madrid had also been keeping tabs on the forward's situation, but they are unlikely to make a move, with Paris Saint-Germain's Kylian Mbappe expected to join the club ahead of next season.
Williams has made 112 senior appearances since coming through the youth ranks at Athletic, scoring 18 goals and contributing 18 assists.