The bidding deadline was December 3.
SOD intended to sell the stake in the telecoms operator in order to raise money to reimburse people who invested in the telephone network in the 1980s and in the early 1990s, STA reported.
Having failed to sell the 10% stake, SOD now needs to explore other options to secure the money for reimbursements. It has already proposed that the government, in effect, buy back the stake, STA added.
The government owns some 74% in Telekom Slovenije directly or via its funds. Local and foreign shareholders hold the balance.
Telekom Slovenije's shares rose 1.62% to an average price of 148.67 euro ($189) on the Ljubljana Stock Exchange on Wednesday.
($ = 0.7871 euro)