The Sky Sports pundit is backing an away win but feels the Magpies will still provide a big threat against Ronald Koeman's side.
The duo face off at St James' Park in Saturday's late kick-off, with Southampton sitting third in the table after winning their first game at Old Trafford for 27 years last weekend.
Newcastle, meanwhile, are still without a full-time manager since Alan Pardew left the club, with John Carver in caretaker charge on Tyneside.
Redknapp, though, has warned that the Magpies are capable of producing a big performance, while he feels Carver's determination to prove himself will also count against the Saints.
Intriguingly, however, the Sky Sports pundit is still backing a 2-1 Southampton win.
"Newcastle, who were incredible for 40-odd minutes against Chelsea last week and could have been 2-0 or 3-0 up, have proved this season they can produce big performances," he said.
"And they have a caretaker manager in John Carver who will be desperate to get a win, to show he can do the job full-time.
"I think Southampton will just pip a tight game 2-1, though, and earn another three points towards their dream of Champions League football."
There is perhaps no element of shock as such to Redknapp's verdict, with Southampton flying high so far this season. As the pundit himself states, though, Newcastle will be determined to finally get back to winning ways.
An exciting clash hopefully awaits, with both sides having all to play for.