According to SowetanLive, the South African Football Association (Safa) technical committee has trimmed the candidate list down to two men - Queiroz and Renard.
The former Manchester United assistant manager is no stranger to South African football, having held the same position between 2000 and 2002.
He was in the running for the job in 2014, but he eventually lost out to Shakes Mashaba.
Renard on the other hand, is one of the respected coaches on the continent having won two Afcon titles with two different countries - Zambia (in 2012) and Ivory Coast (in 2015) in the last five years.
The country's FA was expected to announce the new coach on the 28th of February 2017, but Safa's communications manager confirmed this week that Bafana will have a new coach by Friday the latest.
While Queiroz is the preferred choice, his high salary demands could force Safa to go for Renard. The length of the contract is reportedly another issue that's being considered by Safa.
Queiroz was reportedly earning around R20-million a year as Iran coach, and he's believed to be demanding around that region to sign on the dotted line with Safa - hence the delay.
Safa made it clear that one of the mandates for the incoming coach will be to qualify for the 2018 Fifa World Cup in Russia, while the new man will also be expected to do well in the upcoming 2019 Afcon campaign which kicks off in June this year.
The association is determined to fill the position before this month's (March) international friendly matches against Angola and Guinea-Bissau in Durban and Bloemfontein respectively.