"He who finds a wife finds a good thing and obtains favour from the LORD." - Proverbs 18:22.
After an extensive investigation, SA Airlink dismissed the claim and said its employees were blameless, Beeld reported.
According to the newspaper, the airline said it could find no evidence of tampering with Madiba-Zuma's luggage.
The theft allegedly occurred on December 15, 2012, when Madiba-Zuma flew from Nelspruit Airport to OR Tambo International Airport and was driven by car to Bloemfontein to join her husband for the ANC's conference in Mangaung.
On December 18, she drafted a statement in which she declared that 36 pieces of expensive jewellery had gone missing from a cosmetics purse inside an unlocked, orange Cellini bag.
"After we arrived [in Bloemfontein], we rushed to get ready for a dinner. That's when I first opened my suitcase and realised that the cosmetics purse with all my exclusive jewellery was gone," Madiba-Zuma reportedly said in a statement submitted to SA Airlink on January 5.
According to Beeld, SA Airlink head Rodger Foster rejected the claim after viewing the CCTV footage available.
"We compelled all employees to undergo polygraph tests, which showed that they were not involved in the alleged theft of Mrs Zuma's valuables," Foster reportedly wrote in a letter to the presidency.
Beeld reported that SA Airlink had declined to comment on the issue.
It reported that, in an e-mail addressed to journalists on Sunday night, Madiba-Zuma said she had instructed her lawyers to consider her legal position and advise her accordingly.
"The investigation continues.... I will wait for my lawyers' final advice before I decide what to do. My personal jewellery was, unfortunately, not insured," Madiba-Zuma reportedly said.