The Spanish Under-21 star has been linked with a move to Merseyside in recent weeks and has now apparently appeared on the radar of Arsene Wenger.
Williams has had a breakthrough season at Bilbao, already scoring 10 times in La Liga despite playing on the right-hand side on midfield - though he is equally as comfortable as a front man.
He made the headlines earlier this season after his superb goal against Espanyol left plenty of football fans' jaws routed to the floor - and what flick over a defender followed by a rocket of a volley wouldn't?
The 21-year-old currently has a £15.3 million release clause in his contract, so the trio of Premier League clubs will know they won't need to get into a bidding war with the Spanish side.
However, they are actively trying to move the clause up to a reported £76.3 million, meaning teams will have to act fast if they want to save a few pennies on the talented player.
While he is very powerful and has a good eye for goal, Williams' greatest assest may just be his pace. He's already broken the record for the fastest La Liga player ever, reaching speeds of a rather ridiculous 22.2 mph last season.
With Arsenal looking to continue their push for the Premier League as well as retaining the FA Cup and getting further into the Champions League, adding Williams to the ranks might just give them the depth to do so.