Former Zanaco forward Phiri reportedly started training with the Telkom Knockout champions on Monday along with new signing Deon Hotto, who left Bloemfontein Celtic as a free agent.
"A Zambian player by the name of Moses is also training with Wits," says a source at the Students.
According to the informant, the club are still assessing midfielder Buyani Sali following his arrival at Sturrock Park on Saturday. Sali parted ways with Chippa United at the end of last term.
Meanwhile, Klate has not been at Wits' pre-season training, fuelling speculation the decorated veteran is on the way to known admirers Chippa following the expiry of his contract in Johannesburg.
The Clever Boys recently added Bantu Mzwakali, Mxolisi Macuphu and Brighton Mhlongo to their roster ahead of 2018/19.