Williams, wearing the armband in absence of Craig Bellamy, turned his ankle in the latter stages of Friday's loss to Bulgaria at the Cardiff City Stadium.
The Swansea defender was given the all-clear to travel to Basle after an X-ray on Saturday and has shown considerable improvement since, playing a full part in training today.
Caretaker manager Brian Flynn said: "His ankle has got better every day and I am very confident he will be able to start."
Flynn must make changes in defence with Chris Gunter and Sam Ricketts both suspended.
Cardiff's Darcy Blake, 21, will win his first cap at right-back while Williams, if fit, is likely to revert to his natural centre-half position after playing in midfield last week.
Flynn has further defensive options having drafted in Rhoys Wiggins of Bournemouth on Saturday and then making a further late addition to his squad by calling up Preston's Craig Morgan yesterday.
Flynn added: "Darcy will play at right-back. I've seen a lot of him in that position and I like him there.
"I've brought Craig in for his aerial ability, his strength and his power. He will be a good addition to the squad and he will help us."
Flynn also revealed Gareth Bale and James Collins suffered minor strains in the Bulgaria loss but both have been overcome.