Jali, who also played in the colours of Orlando Pirates and overseas with Belgian outfit KV Oostende, is a free agent after his contract with the Brazilians expired at the end of the season.
The 33-year-old had been linked with a return to Pirates or a move to Swallows, but according to reports it now appears City are frontrunners to secure the 44-capped Bafana international’s signature.
Jali’s agent Mike Makaab confirmed his client’s future will be finalised imminently.
“We’re very close to finalising a deal, but I can’t disclose the club.
“I’m hoping that by the end of the week, we will have concluded,” Makaab told FARPost.