The ruling African National Congress' top-level National Executive Committee, many of whom are Zuma loyalists, meets this weekend to consider the way forward.
Zuma, who is in line to run for president next year and will likely ride his party's dominance to power, has long claimed that he was the victim of a political vendetta orchestrated by Mbeki.
Last week, a judge threw out corruption charges against Zuma and implied that Mbeki's government put pressure on the National Prosecuting Authority to bring the charges for political motives.
Zuma himself has not joined the calls for Mbeki to quit, apparently preferring him to see out the dying days of his administration and then withdraw from the political stage.
Newspapers quoted Zuma over the weekend as saying that he didn't want to waste his energy on a "dead snake."
