South Africa's elite Hawks unit has been investigating the allegations against Mr Malema for months.
The authorities have refused to comment in public on reports about the arrest warrant, but lawyer Nicqui Galaktiou says they have confirmed it to her.
Mr Malema, once a close ally of President Zuma, is now a fierce critic.
He strongly denies allegation he profited from government contracts in his home province of Limpopo.
According to the weekly City Press newspaper, he will be charged with fraud, corruption and money-laundering.
Ms Galaktiou told Reuters news agency Mr Malema would appear in court next week and would not be jailed or arrested before then.
"We don't have a confirmed date yet. We have not seen the warrant of arrest. We don't know what the charges are," she said.