Mtshali, who has also played for Free State Stars, is a free agent following the expiry of his contract with Celtic at the end of last month.
"Mtshali is here at Wits," a source close to the Students tells KickOff.com.
"He is training with the club and it looks like he will sign."
The Students recently recruited ex-Orlando Pirates goalkeeper Brighton Mhlongo to provide competition to Bafana Bafana international Darren Keet.
Wits have also also brought in Gift Motupa, Deon Hotto, Bantu Mzwakali and Mxolisi Macuphu.