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"Allianz is on the short list in the sale process for the insurers," Koc chief executive Bulent Bulgurlu told the Financial Times Deutschland newspaper.
Analysts estimate the value of the two insurance companies at 1.2 billion dollars, the report said.
In Turkey, Yapi Kredi Emeklilik holds around seven percent of the life insurance market and almost 16 percent in pension insurance, while Yapi Kredi Sigorta has a market share of around six percent in property insurance, the newspaper added.
Allianz declined to comment on the matter, the FT said.
In April, Allianz also said it was paying nearly $600 million to raise its stake in two Turkish insurers -- Koc Allianz Sigorta AS and Koc Allianz Hayat ve Emeklilik -- for a majority share. The valuation of that deal gave insurance sector shares a boost.
Allianz bought the shares from Koc Holding, along with Unicredit, and is also the main shareholder in Yapi Kredi Bank.
Turkey's insurance sector has seen a wave of foreign acquisitions in the last couple of years, and foreign firms already in Turkey include France's AXA, Britain's Aviva and Spain's Mapfre. The sector's premiums grew 14 percent last year, according to data from industry body TSRSB.