The Welsh club are already without Neil Taylor (broken ankle), Kyle Bartley (thigh), Chico Flores (suspension) and Garry Monk (back), with Alan Tate and Ben Davies coming into the side for the defeat at Aston Villa.
Williams is now struggling with an ankle problem, and midfielder Kemy Agustien, who would have been a candidate to replace the centre-half, has been ruled out with a calf injury.
Williams has had a difficult few weeks. Uncharacteristic errors from the 26-year-old cost Swansea goals against Villa and Sunderland, while he was part of the Wales side humbled 6-1 by Serbia.
But Michael Laudrup insists he remains a key figure for the Swans and is desperately hoping he comes through a fitness test.
"I have spoken to him like I always speak to my players," said Laudrup.
"He has had a difficult week and has not been able to do much because of his ankle, but he will hopefully be fit. It is important for us that our captain is there.
"He had made mistakes but players are allowed to make mistakes and are permitted to have bad games because the important thing is that they give their all and they play in the way we want them to. Mistakes can happen."
Laudrup may also make changes in midfield with record signing Pablo Hernandez and Ki Sung-yueng pushing for their first starts for the club.
Moving Spain international Hernandez into the side at the expense of Wayne Routledge or Nathan Dyer would be harsh on the pair, who have excelled during Swansea's bright start to the campaign.
But Hernandez turned in a promising cameo as a substitute against Villa, and Laudrup said: "It is possible he could start.
"In Pablo, Nathan and Wayne we have three very good wingers and they are a great trio, but there are only two positions so it is true the third one will be on the bench.
"But they all know we have a lot of confidence in them. I am still thinking about who will play but whatever I do I know we will have two quality players in the starting XI."
Of Ki, Laudrup added: "He is fitting in very well with what we want to do.
"I am still getting to know him and see what he can do in training but I think he can play both positions in the centre; in the holding role like Leon (Britton) and the more dynamic role that Jonathan de Guzman has been playing, so it allows us to rotate."
Everton have made a good start to the season themselves, their draw against Newcastle leaves them level on points with the fifth-placed Swans.
And Laudrup is fully aware of the challenge David Moyes' Toffees will pose.
"It is a big challenge for us against a club who have a lot of continuity on the pitch and off the pitch.
"David Moyes has been there 10 years so everyone knows exactly what is wanted of them. They are strong with a lot of individual quality, especially on the left side where they are very good with Leighton Baines and Steven Pienaar.
"And everybody knows about (Marouane) Fellaini who is a difficult player to mark in particular in the last third. They are a strong side but we have a lot of confidence and we know what we are capable of."