The Hammers are currently six points clear of the relegation zone, and with a game in hand on the majority of the teams below them, O'Neil believes that the club will be safe with a victory at St Mary's Stadium on Saturday.
O'Neil told the club's official website: "I think we're looking for one more win. Hopefully, it can come this week but Southampton are in great form and they have had some fantastic results at home.
"It'll be a tough game because they've got some good players. We'll go there and hopefully we'll have a couple more players fit and the gaffer will have stronger squad to pick from.
"Our away form has picked up with a win at Stoke and a draw at Anfield after five straight defeats on the road. Hopefully our improved form can continue."
West Ham have picked up seven points from their last four league fixtures.