South Africa captain Faf du Plessis remains a doubt for the first test against England at Lords starting on 6 July.
Du Plessis is at home with his wife Imari following the birth of their first child on 23 June, but has not yet set a date to fly to England, Cricket South Africa said on Friday.
After what officials described as a "difficult birth", du Plessis will remain in South Africa for the foreseeable future and could miss the game at Lords.
Head coach Russell Domingo is back in England after he returned to South Africa following the news his mother has seriously injured in a car accident a week ago. She has since been discharged from hospital.
South Africa are currently in the second day of a three-day warm-up match against England Lions, where the side is being captained by Dean Elgar in the absence of du Plessis.