Cardiff City (6-8-19) are second from bottom and six points from safety after winning just two of the 13 matches played under Solskjaer, who was appointed Bluebirds manager on Jan. 2 as replacement for the sacked Malky Mackay.
"We need to produce a miracle to stay up now," said Solskjaer after his club's latest defeat, a 3-0 home loss against Crystal Palace last weekend. "I am full of fight. It has been a tough season for everyone involved with the club.
"There was a lack of belief a little bit towards the end. We ran out of ideas. Players are desperate to perform. Of course they want to stay in the league."
The former Manchester United striker claims he still has the backing of Cardiff owner Vincent Tan following the emphatic defeat against Palace.
Cardiff travel to play the Saints at St Mary's having won just one of their 16 away matches in the Premier League.
Southampton (13-9-11) are comfortable in eighth place and well clear of relegation worries. Saints boss Mauricio Pochettino is rated one of the brightest young managers in the Premier League and has produced an attractive football-playing side based around a crop of outstanding young English-born players.
The Saints won three of their past five league matches but were beaten 4-1 at title-chasing Manchester City last Saturday. Pochettino's side were aggrieved that City's second goal scored by Sami Nasri was not ruled out for offside, but the result was overshadowed by a serious knee injury to striker Jay Rodriguez.
It was later confirmed than 24-year-old England international Rodriguez had ruptured his ACL and will be sidelined for at least six months. Rodriguez has scored 17 goals in 45 appearances in all competitions for Southampton this season.
"Forget the decision for the offside, forget the result - forget everything," said the Saints skipper Adam Lallana. "We're just disappointed for our teammate getting injured.
"We're all absolutely devastated for him - he's an unbelievable lad. He's proven this season what a player he is and he's got his rewards internationally. We've all let him know how sorry we are for him."
Rodriguez's absence may give Gaston Ramirez a chance to finally show his true worth. The Uruguayan striker, who was Saints' record signing when he joined for £12 million from Bologna in August 2012, has yet to fulfill his potential at St Mary's with only one goal and three assists in two league starts and 17 matches overall.
Cardiff will be without winger Craig Noone, who is likely to miss the rest of the season with an abdominal injury.
Southampton thrashed Cardiff 3-0 at the City Stadium on Dec. 26 in this season's reverse fixture. Rodriguez scored twice and Rickie Lambert added a third to secure an easy three points for the Saints.