Amakhosi have been active in the current Transfer Window - signing Chicken Inn defender Teenage Hadebe and former Maritzburg United full-back Philani Zulu.
The Soweto giants have now been linked with Bereng, who was one of the Chilli Boys' key players during the 2016/17 season.
The 26-year-old attacking midfielder, who has also been linked with SuperSport United, made 18 appearances in all competitions - scoring goal in the process.
According to recent reports, Amakhosi are said to have joined SuperSport in the race for Bereng, who joined Chippa from National First Divison (NFD) club Cape Town All Stars in July, 2016.
However, the former Moroka Swallows midfielder is still left with two seasons on his contract with the Chilli Boys.
Amakhosi, who have a good relationship with the Chilli Boys, will have to purchase from the Eastern Cape-based outfit.
William Twala and Joseph Molangoane joined Chiefs from Chippa in the last two seasons.