Last weekend's goalless draw at Liverpool edged the Londoners further towards the 40-point mark Allardyce believes will guarantee another season of Premier League football.
Victory at St Mary's would take them through that threshold, but in the way are hosts who have beaten Liverpool and Chelsea in their last two games and also go into the weekend on 37 points.
Allardyce told the club website: "They will be full of confidence. The fans will be expecting to beat us, there's no doubt about that, after they've just beaten Liverpool and Chelsea at home.
"I think we'll just be the next step on the ladder for them to beat. I thought the Liverpool fans probably thought they were turning up and going to beat us last week, so we'll hopefully spoil Southampton's party as well."
No team since West Ham's 2002/3 vintage has been relegated with 40 or more points, and Allardyce said: "If we win it, I think we'll be safe.
"I know mathematically people will say we can still be caught and somebody could still overtake us but I find it difficult to believe that anybody would.
"Over the 20-odd years there are only a few cases of teams going down with 40 but it has been a long time since that was actually the case."
Andy Carroll - ineligible at Anfield under the terms of his loan - is back in the squad for Saturday but faces a fight to regain his place.
Allardyce said: "Whether I am going to select Andy or keep Carlton Cole in is a little dilemma because I thought Carlton did ever so well last week. I suppose had Carlton scored, I would have definitely kept him, but he didn't."