The former England boss succeeded Frank de Boer as Palace manager earlier this week and he takes over a club that are yet to register a point or goal in the Premier League this season.
No top-flight side has ever lost their opening five league matches without scoring a goal, but the omens are not good for Palace, as they have failed to score in eight of their last nine league games, a run that stretches back to last season.
The Eagles have won their last two home matches against Southampton, however, with Christian Benteke netting a brace the last time the two sides met at Selhurst Park last December.
Benteke is expected to lead the line for Palace once again on Saturday, although Hodgson could be tempted to make changes to his side, with deadline day signing Mamadou Sakho pushing for his first start since re-joining the club on a permanent basis.
Southampton will also head into the match knowing they need to start scoring on a more regular basis, as they have failed to net in nine of their last 12 league matches.
Mauricio Pellegrino's side have also failed to win any of their last three games in all competitions, although they are unbeaten in their last three league fixtures away from St Mary's Stadium.
Pellegrino must decide whether to recall centre-back Virgil van Dijk, who has not featured for the first-team since January due to an ankle injury, while he also tried to force through a move away from the club during the summer.
Midfielder Pierre-Emile Hojbjerg will definitely not feature, as he has been given time off following the birth of his daughter.