The Saints will welcome Marcelo Bielsa's outfit to St Mary's on Saturday afternoon in the Premier League as they search for a first win of the campaign.
Hasenhüttl was already set to be without club captain James Ward-Prowse due to suspension but will also be missing striker Che Adams.
The forward picked up a muscle injury whilst away with Scotland on international duty and will now miss this weekend's top flight encounter against the Whites.
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"Jack Stephens is still out," the Southampton boss told his pre-match press conference on Thursday.
"Che Adams returned back with a muscle injury, it's not too serious but he's definitely out [against Leeds]. I've not seen everyone [international players] so far but the reports are good."
Saints skipper Ward-Prowse was called into the England squad as a replacement for the injured Kalvin Phillips last week but will be absent against the Whites this weekend.
The midfielder was sent off against Chelsea - a decision which required VAR intervention - in his side's last fixture for a rash challenge on Jorginho at Stamford Bridge.
He will serve the first game of his domestic ban against Leeds this weekend in what is a tough blow for Hasenhüttl after 102 consecutive outings for the hosts.
Ward-Prowse is Southampton's on-pitch leader alongside being the club's set-piece specialist - having scored some stunning free-kicks in recent seasons, including finding the back of the net twice already this season.
Adams' absence up front is set to hand Armando Broja a first Premier League start for the Saints, who are expected to play with two strikers.
William Smallbone also remains out as he continues to step up his recovery after rupturing his anterior cruciate ligament around nine months ago.
Defender Stephens still has a number of weeks to go in his recovery from a tendon knee injury picked up against Manchester City last month.