Both have not featured since the opening day of the season after Godfrey broke a leg and his defensive counterpart Mina injured a calf.
Right-back Nathan Patterson could come back into the side after a substitute appearance last weekend on his return from injury.
Leicester boss Rodgers will make a late call on Evans as he works his way back from a calf injury.
Evans has not played since the 2-1 defeat by Bournemouth on October 8, but has been back in training and Rodgers suggested he would be ready to return for Tuesday's Carabao Cup match against Newport if he did not make the squad on Saturday.
Ricardo Pereira has made progress on his return from a ruptured Achilles but will not return until after the World Cup.
Everton provisional squad: Pickford, Patterson, Tarkowski, Coady, Mykolenko, Onana, Gueye, Iwobi, Gordon, Calvert-Lewin, Gray, Begovic, Keane, Coleman, Vinagre, Holgate, Doucoure, Davies, Garner, McNeil, Maupay, Rondon.
Leicester provisional squad: Ward, Iversen, Smithies, Vestergaard, Faes, Evans, Amartey, Justin, Thomas, Castagne, Soumare, Dewsbury-Hall, Maddison, Tielemans, Barnes, Albrighton, Praet, Vardy, Daka, Iheanacho, Perez.