Alexis had missed last weekend's 2-1 defeat to Watford, while Ozil hasn't started a match for the Gunners since September 9.
Repeated calls have been made for Jack Wilshere to return to Arsene Wenger's starting XI, but the in-form Englishman must settle for a spot on the bench this afternoon, with Aaron Ramsey and Granit Xhaka preferred in the centre of the park.
Arsenal one again line up with three centre-backs, with Sead Kolasinac and Hector Bellerin taking up the wing-back positions in a 3-4-2-1 formation.
The Gunners can go level on points with fourth-placed Chelsea with a win at Goodison Park, while defeat for the hosts will undoubtedly see fans calling for the sacking of Ronald Koeman with the Toffees hovering just above the relegation zone.
Everton XI: Pickford, Kenny, Keane, Jagielka, Williams, Baines, Gueye, Vlasic, Sigurdsson, Rooney, Calvert-Lewin
Everton Subs: Robles, Mirallas, Martina, Niasse, Klaassen, Davies, Lookman
Arsenal XI: Cech, Koscielny, Mertesacker, Monreal, Bellerin, Ramsey, Xhaka, Kolasinac, Ozil, Lacazette, Alexis
Arsenal Subs: Macey, Holding, Coquelin, Wilshere, Iwobi, Walcott, Giroud