The former deputy president of South Africa and key member of the ruling African National Congress, Baleka Mbete, said pressure was being applied by "interested parties" to bring about a resolution to the country's current crisis.
"I think that it is the issue that is going to be behind us quite soon... I think early in this coming week it should be clearer, after more consultations that will happen over the weekend," Ms Mbete, who currently serves as speaker of South Africa's sometimes-raucous National Assembly, said.
"Hopefully early in the week we should be utterly able to indicate we're moving on."
Mr Zuma is deeply unpopular with many South Africans after serving eight years as the nation's President.
He has been accused of multiple accounts of corruption and the country's highest court said he violated the constitution when he failed to repay money spent on his private home. Eventually, he repaid an amount calculated by the finance ministry.
It is now the task of ANC party president Cyril Ramaphosa to manoeuvre Mr Zuma out of the door and prepare this fabled organisation for a national election next year.