Gigaba said they have interviewed candidates for the position, and the SAA Board has shortlisted candidates.
The board would now go for the final round of interviews before picking a successful candidate.
In a written reply to Parliament Gigaba also revealed that they have appointed the Chief Financial Officer, but declined to give the name.
He said the board had finalised the process of selecting the CFO, after the interviewing process of several candidates.
He also would not say how soon the announcement on the name of the new CFO would be made.
The national carrier has been without a permanent CE after Monwabisi Kalawe left the airline after disciplinary issues and a settlement.
He was paid a remainder of contract in his settlement with SAA after the matter of his disciplinary went to the Labour Court in 2015.
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SAA CFO Wolf Meyer also quit immediately after Kalawe’s departure.
Meyer resigned from SAA in 2015 after a reported breakdown of trust with the then board.
The national carrier has been without the top officials in the past two years.
When the new board of SAA was appointed by Cabinet last year former Finance Minister Pravin Gordhan said one of its tasks was to ensure stability of the airline and the filling of the critical posts.
BUSINESS REPORT ONLINE