On Tuesday, the constitutional court found him guilty of contempt for defying its order to appear before a corruption inquiry.
A deadline for his arrest had been set for midnight on Sunday.
However, the constitutional court later agreed to hear his challenge to the 15-month jail term he was given.
Just how that affects the arrest deadline is unclear.
“[There is] no need for me to go to jail today,” Mr Zuma, 79, told reporters outside his home in Nkandla in Kwa-Zulu Natal province on Sunday.
“Sending me to jail during the height of a pandemic, at my age, is the same as sentencing me to death,” he added.
He said he had been “lambasted with a punitive jail sentence without trial” and that “South Africa is fast sliding back to apartheid rule”.
One supporter, Lindokuhle Maphalala, told AFP news agency that if the police chief came to arrest Mr Zuma “he must start with us”.
The court has said it will consider Mr Zuma’s appeal on 12 July.
In the meantime, another appeal against the arrest order is expected to be heard by the high court of KwaZulu-Natal province on Tuesday.
The 79-year-old political veteran was ousted in 2018 after nine years in power, amid corruption allegations.
Businessmen were accused of conspiring with politicians to influence the decision-making process.
But Mr Zuma has repeatedly said that he is the victim of a political conspiracy.
The former president testified only once at the inquiry into what has become known as “state capture” but then refused to appear subsequently.
In a separate legal matter, Mr Zuma pleaded not guilty last month in a corruption trial involving a $5bn (£3bn) arms deal from the 1990s.
Source: BBC
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