The Toffees are eighth in the table and did not lose a game in April, but Allardyce has come under heavy criticism for the team’s performances.
Despite a 2-0 win against Huddersfield last weekend, Everton supporters have called for Allardyce to be sacked. The manager has argued he can’t do any more than what he’s doing.
Southampton snapped a five-game winless streak with a 2-1 victory over Bournemouth last Saturday to move one point adrift of safety with three games to play.
Saints demolished Everton 4-1 when the teams faced each other at St Mary’s in November.
Dominic Calvert-Lewin’s back injury will see him miss the remainder of the season for Everton.
James McCarthy, Eliaquim Mangala and Gylfi Sigurdsson all remain on the sidelines.
Steven Davis is unlikely to feature for the visitors having suffered a recurrence of an achilles injury.
Predicted starting line-ups:
Everton: Pickford, Coleman, Jagielka, Keane, Baines, Gueye, Schneiderlin, Vlasic, Rooney, Walcott, Tosun.
Southampton: McCarthy, Soares, Bertrand, Bednarek, Yoshida, Hoedt, Romeu, Lemina, Tadic, Redmond, Austin.
Odds: Everton 19/10, Southampton 6/4, Draw 11/5.