Johannesburg - "The announcement will be made, but it has been postponed," SAFA communications director Morio Sanyane said on Sunday.
A kit sponsor was expected to be named on Monday but the press conference was postponed at the last minute.
The national football team has been without a sponsor since SAFA ended a 12-year partnership with sports equipment and apparel manufacturer Adidas in November.
Former SAFA CEO Leslie Sedibe said before he stepped down from his post last week that Puma would be named as the new sponsor in time for South Africa's friendly match against Kenya at Royal Bafokeng Stadium on Wednesday.
Bafana Bafana were set to arrive in Rustenburg on Monday, in preparation for the match which was initially expected to be played against Burkina Faso, after a week of commotion within the SAFA administration.
SAFA president Kirsten Nematandani admitted earlier this week that a contract was never signed with Burkina Faso and the West African nation withdrew from the agreement on the eve of the match.