The attacker is impressing for Spain at the Euros, where he has been scouted by the Blues.
After being beaten by Bayern Munich to the signing of Crystal Palace attacker Michael Olise, Chelsea are turning to Williams, reports Sky Italia's Gianluca di Marzio.
And the Blues aren't going to wait around and intend to meet the €50m buyout clause in Williams' deal.
However, the youngster may need some persuading, having stated just last week: “I’m very happy at Athletic, it’s the club that has given me everything.
"It’s the club that has bet on me 100 per cent. I’m very happy in Bilbao and that’s what I have to say.
“Yes, I am quite clear about it. Athletic is my home, I am very happy, now what I want to do is focus on the Euros. If you are not 100 per cent in a competition for this one, they will overtake you. As for the rest, I don’t know what will happen.”