Sangweni's agent, Ali Tlhoaele has confirmed that at least five teams have called him to enquire about the player's availability, but claims he referred them to the Chilli Boys.
The 28-year-old is contracted to Chippa United for the next three years, meaning whoever wants the player will have to meet Chippa Mpengesi's asking price first.
Despite confirming interest in his client, Tlhoaele couldn't be drawn into disclosing the names of the teams that are chasing after the former Mamelodi Sundowns midfielder.
"I can confirm that I had big five teams in South African football calling me, enquiring about Thami. Unfortunately I can’t name those teams," Tlhoaele told SunSport.
"I told them to talk to his club because the player still has a contract with them," he confirmed.
Tlhoaele pleaded with the teams interested in Sangweni not to contact the player directly, as he claims this has been the case.
"I heard that other teams are also calling the player. We need to respect that the player is under contract with Chippa and anyone interested must talk to them," he concluded.
Last week, Amakhosi parted ways with Lucky Baloyi among other players, and reports suggest that they have earmarked Sangweni as a possible replacement.
They currently have Willard Katsande, George Maluleka and Keagan Buchanan as their three central midfielders, and whether or not they will be stepping up their chase for Sangweni remains to be seen.