It is understood that Zuma wants the state to cover his legal costs in the event of prosecution but that Ramaphosa is reluctant to agree to this without co-operation from the president in pinning down those who were involved in capturing the state.
The Sunday Times has also learnt that Ramaphosa intends to appoint Housing Minister Lindiwe Sisulu as his deputy when he becomes president.
She will become the second woman to occupy the post.
Ramaphosa apparently settled on Sisulu as deputy president after exploring the possibility of naming Science and Technology Minister Naledi Pandor to the post.
The Sunday Times has learnt that Ramaphosa consulted allies about appointing Pandor, who he named as his preferred deputy during his campaign for the ANC presidency last year — a choice that took many people by surprise.
• Read the full story on the Sunday Times website