The attacking midfielder's current Sundowns deal is due to expire at the end of this season and he is reportedly yet to be offered a contract extension.
It is said that Chiefs are monitoring his situation at the Chloorkop-based side, while an unnamed foreign club is also interested in Zwane.
The Bafana Bafana international, who has established himself as one of the top midfielders in the country, was recently linked with top PSL sides SuperSport United and Orlando Pirates.
Zwane netted nine goals in all competitions last season and he played an instrumental role in helping Sundowns win the 2016 Caf Champions League title.
With interest reportedly mounting in one of their prized assets, the Brazilians are likely to open contract extension talks with Zwane soon.
The 28-year-old player, who is technically gifted, joined Sundowns in 2011 after the club beat Pirates to his services.
He spent the 2013/14 season out on loan at Mpumalanga Black Aces, who are now known as Cape Town City.