The 29-year-old is under severe pressure as Pakistan have lost three matches on the trot and a defeat to the rampant South Africans would virtually knock them out of the semifinal race.
Pakistan need to win each of their remaining four league stage games and also hope that the other results go their way in order to make the semifinals.
The Pakistan Cricket Board released a statement earlier in the day urging fans to stand by the team, but also claimed it would take all necessary decisions for the improvement of the national side, which has fallen short on many counts in this World Cup.
The PCB said both Babar and chief selector Inzamam-ul-Haq were given "freedom and support in forming the squad for the ICC World Cup 2023".
It was right after the statement that Pakistan's training session began in Chennai, during which Babar largely kept to himself.
After a 30-minute fielding session, he was the last to arrive in the nets to bat.
He appeared to be taking a reserved approach, sitting down for a chat with the support staff before heading into the nets and facing seamers and throwdown specialists. Opening batter Imam-ul-Haq was also seen having a chat with Babar.
Imam and Fakhar Zaman also had a hit against the local seam and spin bowlers.
With his slingy bowling action, Zaman Khan was seen assisting the batters in their preparations even though South Africa do not have any such bowler in their ranks.
Zaman is still yet to gain full fitness from the knee injury that he suffered right before the competition.
Although the left-handed batter had a long session on Wednesday, he batted only for a short while on Thursday and is unlikely to be drafted to the playing XI.
The Pakistan management is likely to give Imam another chance with the batter getting into double digits in each of the five games in this World Cup but managing only one fifty.
However, sources indicate that spinner Usama Mir is all set to be replaced by Mohammad Nawaz, with the side preferring a finger spinner on the slow Chepauk surface.