"Selhurst Park isn't an easy place to go," Davis told Southampton's website.
"We'll be expecting their players, with a new manager potentially coming in, to give their best and try to get themselves out of the position they're in now."
Palace have lost all four of their games without scoring and are poised to appoint former England manager Roy Hodgson as De Boer's replacement, according to reports in the British media.
Southampton have also made a slow start and suffered their first league defeat of the season at home to Watford on Saturday.
The south coast club have five points but have not scored in three of their four games so far. Davis said they have plenty of room for improvement following their limp display in the 2-0 defeat by Watford.
"There's a lot of anger and disappointment with the way we played but we need to stick together now," he said.
"We've got a lot more quality than what we showed against Watford and it's about going out and proving that now."
Southampton's last league trip to Selhurst Park ended in a 3-0 defeat last December, but the team could be boosted by the return of defender Virgil van Dijk, who played 90 minutes for their youth side on Monday.
The Dutchman has not played for the first team this season since failing to force through a move to Liverpool.
(Reporting by Aditi Prakash in Bengaluru; Editing by Keith Weir)
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