ETHNIKI's sale is part of a larger restructuring plan approved by Greece's second largest lender by assets with regulators, to exit non-banking operations.
"Two months until the end of 2018 is potentially not enough to complete the plan," one of the sources, who declined to be named, told REUTERS.
"NBG is preparing a proposal on the time frame it wants to conclude its divestments plan," the source added.
ETHNIKI Insurance is Greece's largest insurer in the country, with a presence in Romania, Bulgaria and Cyprus as well.
In June 2017, the National Bank of Greece's board approved the sale of 75% stake in ETHNIKI Insurance to the American-Dutch consortium CALAMOS-EXIN after bidding about EUR 718 million.
Other bidders were the Chinese conglomerate FOSUN and Shanghai-based GONGBAO.
The NBG declared the tender barren after the sale of ETHNIKI to CALAMOS-EXIN failed because the purchase amount of EUR 718 million had not been paid by the end of March 2018.
The second sale attempt failed about two weeks ago, when the NBG ended negotiations with the Shanghai-based GONGBAO Group on the sale. GONGBAO was the only bidder in the final stage of binding financial offers for the buyout of a 75% stake in Greece's leading insurer.