According to sources, Zungu will leave Sundowns at the end of the season.
The 22-year-old Bafana Bafana midfielder has been the topic of speculation, with a number of local and international clubs inquiring about his availability.
Downs have been looking to tie down Zungu since last year but he will not be signing a new deal with the club.
Phakaaathi sources at the club have revealed Downs have offered Zungu an improved deal and are hoping the midfielder will change his mind before the season ends.
Primeira Liga outfit Vitoria de Guimaraes had a R6 million offer for Zungu rejected during the previous transfer window.
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