The Italy international could start on the bench for Mauricio Pochettino's side, while Greek winger Charis Mavrias could make his first appearance under Paolo Di Canio
Osvaldo, who signed from Roma on Sunday for an initial £12.8 million fee which could rise to £14.5m after bonuses, is in line to play some part in the fixture against Paolo Di Canio's side.
But it will not be from the start, with Pochettino cautious of throwing his star man in at the deep end.
"He played an international match last week with Italy, so he is fit," Pochettino told the club's official website.
"It's also logical that he needs to establish and integrate himself into a new structure. Also, he needs to learn how Southampton plays.
"He needs to learn a new structure, but we still have one training session left, so after that we will see if he has a chance to get into the 18 players that have been called up for Saturday."
Osvaldo – who scored 28 goals in 57 appearances over two seasons at Roma – replaced Kenyan Victor Wanyama as the club's record signing.
Wanyama, who joined from Celtic for £12.5m in July, played 90 minutes in Southampton's 1-0 win at West Brom last Saturday.
Rickie Lambert scored an injury-time penalty for Southampton at the Hawthorns, with academy graduates James Ward-Prowse and Luke Shaw particularly impressive.
Southampton have a clean bill of health but Sunderland will be without striker Steven Fletcher (ankle) and Lee Cattermole (knee).
Phil Bardsley (foot) remains on the sidelines for Sunderland but Wes Brown (knee) could feature.
Sunderland made a poor start to their Premier League season, slumping to a 1-0 defeat against Fulham at the Stadium of Light.
Sunderland have not won in their last five Premier League fixtures and they travel to Southampton having triumphed just twice on the road in 2013.
Di Canio handed five players their debuts on Saturday, and their busy transfer window continued on Thursday with the signing of Greek winger Charis Mavrias.
The two sides have played each other just four times in the last 10 years, with Sunderland winning two of them, and the others ending in draws.
Southampton's last win against Sunderland came in March 2002 and the most recent meeting finished in a 1-1 draw in May.