Forwards Eben Etzebeth, Bongi Mbonambi and Pieter-Steph du Toit are the frontrunners to captain South Africa against Wales at Twickenham on June 22, head coach Rassie Erasmus said on Thursday.
"It will probably be Pieter-Steph, Eben or Bongi," he told a media briefing in Pretoria, where a 35-man Springboks squad are training.
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Erasmus said a decision would be made on Sunday, 48 hours before the team to face Wales in a one-off Test is announced.
Regular captain and double Rugby World Cup winner Siya Kolisi is unavailable for the one-off international due to commitments with French club Racing92.
Kolisi is among 13 Springboks from the matchday 23 that beat New Zealand in the World Cup final in Paris last October who have been ruled out due to club duties, injuries or suspension.
The loose forward moved to Paris after the 2023 World Cup triumph and Erasmus said he could skipper the team in a two-Test home series against Ireland during July.
Ireland beat South Africa in a pool match at the World Cup last year before the Springboks claimed one-point victories over France, England and New Zealand to achieve back-to-back titles.
"We are going into this Wales Test without Siya and without seeing how he is going to come back from France," said Erasmus.
"We will need to assess him and see how he slots into things. We have two weeks after the Wales Test (before playing Ireland).
"When we announce the Ireland squad, we will announce a captain and obviously a guy like Siya will be in the running if everything goes well and he is injury free.
"To be honest with you, inside the team, the captaincy is not such a big thing. We have a lot of leaders in the group."
Erasmus said earlier this year that he would need to re-evaluate the Springbok captaincy with Kolisi now 32 years old and based in France. Since South Africa were readmitted to international rugby in 1992 after apartheid-induced isolation, the Springboks captain has always been based at home.
Meanwhile, South Africa's double World Cup-winning wing Cheslin Kolbe has rejoined the Springbok training camp in a bid to overcome the injury that has ruled him out of this month's Test against Wales, SA Rugby announced on Thursday.
Kolbe left the camp on Monday for tests on a "knee niggle" that he picked up while playing for his Japanese club Tokyo Sungoliath.
The 30-year-old will miss the World Cup winners' Test against Wales at Twickenham on June 22 but is aiming to be fit to face Ireland in July.
SA Rugby said Kolbe "will do his rehabilitation under the supervision of the Bok medical staff with an eye on possibly being available for selection for the opening Test against Ireland".