"That goes without saying and we want some big scalps this season, we've managed to do that in previous seasons and there's no reason why we can't do it again," Davis told the Southern Daily Echo.
"It's going to be a hugely difficult game for us but we believe we've got the quality to beat any team in the league. We need to show it now," he added.
"Every game in the Premier League, whether it's against one of the top six or any position in the league, it always has its difficulties. You need to be at your best."
United are currently level with leaders Manchester City on 13 points from five games, having scored 16 goals and conceded only two so far.
The 2-2 draw at a raucous Stoke City was the only time Jose Mourinho's side have dropped points this season and Davis said the home crowd could play a role in denting United's unbeaten start.
"It's great if you can create that hostile atmosphere. It gives the home team such a backing as well, and really pushes them on," he said.
"Not only when you're winning or when you're hanging on to the result but whenever you're trying to get that energy from the crowd. You need that."
Southampton, ninth in the table on eight points from five games, last beat United at home in the Premier League in 2003.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by John O'Brien)
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