Meza was spotted together with new signings Andile Jali and Toni Silva as the Brazilians went through their paces at Chloorkop on Monday.
The 27-year-old previously led the line at Oriente Petrolero in Bolivia.
Sundowns are expected to free up two foreign spots to accommodate the arrival of Guinea-Bissau international Silva and another foreign recruit.
According to a source close to Downs, Meza appears to have been added to the playing roster of head coach Pitso Mosimane.
"Pitso has been keeping a close eye on two foreign players, one from Benin and one from North America," says the informant.
"It looks like the deal with Meza has been done.
"He was training with the club at Chloorkop yesterday."
Mosimane's men will resume their CAF Champions League campaign with a trip to AS Togo-Port on July 17, having drawn their first two Group C games against Wydad Casablanca and Horoya AC.