The pair were substitutes for the Merseyside derby win at Anfield and although Calvert-Lewin came on, midfielder Allan has yet to make an appearance since returning from two months out with a hamstring problem.
Centre-back Yerry Mina faces another two weeks out with an ankle injury while long-term absentee Jean-Philippe Gbamin, who has not played since August 2019, is still working his way back to full fitness in training.
Southampton midfielder Oriol Romeu is set to miss the rest of the season because of a fractured ankle, which will need surgery.
On-loan Liverpool forward Takumi Minamino (hamstring) also suffered an injury in Tuesday night's defeat at Leeds, so will miss the trip back to Merseyside.
Forward Theo Walcott, defender Kyle Walker-Peters and midfielder Ibrahima Diallo all continue their recovery from respective thigh problems, while Michael Obafemi and William Smallbone are long-term absentees.
Everton provisional squad: Pickford, Holgate, Keane, Godfrey, Digne, Allan, Doucoure, Gomes, Rodriguez, Calvert-Lewin, Richarlison, Olsen, Coleman, Nkounkou, Davies, Sigurdsson, Iwobi, King, Bernard.
Southampton provisional squad: McCarthy, Bertrand, Vestergaard, Salisu, Bednarek, Jankewitz, Ward-Prowse, Redmond, Armstrong, Adams, Ings, Forster, Stephens, Djenepo, Watts, Ramsay, Ferry, Chauke, Tella, N'Lundulu.