The visit is in the planning stages and will be aimed at discussing ways for Gaddafi to exit, Talk Radio 702 said, citing sources in Tripoli.
Zuma’s spokesman was not immediately available for comment.
France and the United States have made upbeat assessments on progress towards ending Gaddafi’s 41-year rule.
French Foreign Minister Alain Juppe said on Tuesday that the NATO bombing campaign was making progress and should achieve its objectives within months.
France, Britain and the United States are leading the air strikes, which started on March 19 after the United Nations Security Council authorised “all necessary measures” to protect civilians from Gaddafi’s forces as he sought to crush an uprising.
Talk Radio 702 said Zuma will visit Libya after attending the inauguration of Nigerian President Goodluck Jonathan on May 29.
The South African president headed an African Union mission to Tripoli in April but the AU bid to halt the civil war collapsed within hours.
Last week, South Africa accused Libya of misleading it over the fate of a South African photographer now believed to be dead after being shot and abandoned in the desert by forces loyal to Gaddafi.