Club captain Jagielka is available once more after missing nearly a month with a hamstring problem and could replace Williams, whose shaky form continued with a crucial mistake for Wales on Monday.
There is positive news on James McCarthy as he closes in on a return from a knee injury, with Everton set to give him a run out for the Under-23s next Tuesday before welcoming back to the first-team fold.
Boss Ronald Koeman is still without Seamus Coleman, Ramiro Funes Mori, Ross Barkley, Aaron Lennon and Yannick Bolasie due to long-term injuries, but was relieved to see all those players who went out on international duty return unscathed.
Provisional squad: Pickford, Stekelenburg, Williams, Keane, Jagielka, Holgate, Martina, Kenny, Baines, Schneiderlin, Gueye, Besic, Klaassen, Sigurdsson, Rooney, Davies, Vlasic, Lookman, Mirallas, Sandro, Calvert-Lewin, Niasse.
Manchester United are ready to launch a straight £60million bid to try and sign Chelsea star Willian, reports have claimed.
Liverpool are being linked with a swoop for Inter Milan striker Andrea Pinamonti, but have been warned he wants regular action.
Borussia Dortmund are reported to have dropped all interest in Chelsea striker Michy Batshuayi and are looking elsewhere.
Sevilla are bracing themselves for interest in Steven Nzonzi and have lined up a replacement in the form of Marcos Llorente.
Newcastle are targeting a move for Juventus midfielder Stefan Sturaro and are reported to have lodged an opening bid of £11.5million.
Southampton have joined the race to sign Norwich midfielder James Maddison, but will have to move quickly to secure his signing.
Bournemouth are weighing up a move for Sheffield United midfielder David Brooks, but will have to pay £12million to land him.