Mokondelela is a free agent after leaving Pirates a fortnight ago.
"Donald has impressed the technical team," says a source. "The club is preparing to sign him."
City spokesperson Vusi Mtimane confirmed Mokondelela is training with the team but would not comment on whether Rise and Shine will sign the 25-year-old.
Mokondelela joined Bucs at the beginning of last season from Baroka but managed just two substitute appearances before being loaned to Chippa United in January.
He played a further seven times in all competitions for the Chilli Boys before his contract with Pirates was terminated two years before expiry.