"As of now, OeIAG will only hold concluding talks with Lufthansa," it said in a statement after a meeting of its privatisation committee.
Rival bidders "S7 and Air France-KLM are no longer in the bidding process," it added.
OeIAG explained that S7 had failed to submit documents that were in conformity with the EU bidding rules, while Air France-KLM had not made an offer within the allotted time. The two companies have been informed of the holding's decision, it added.
OeIAG director Peter Michaelis said the sale price and details in the deal with Lufthansa would still be finalised in the coming weeks, but added that he expected an agreement within a month, which would allow the holding company's directors to examine the decision at their next meeting on December 5.
Among the issues to discuss are Lufthansa's reported demands that the government take over €500 million ($638 million) of AUA's debt of more than €1 billion.
Lufthansa is offering only a nominal price for OeIAG's 41.6-percent stake - just €0.01 per share or €360,000 ($445,200) in all, according to media reports.
On Thursday evening, Lufthansa refused to comment on OeIAG's decision. At Thursday's close, AUA shares were down 0.38 percent to €2.63 on the Vienna stock exchange.