Aviva began a review of its Asia business earlier this year under new CEO Maurice Tulloch.
"Following a thorough review of options for the Singapore business, including seeking offers ... Aviva has concluded that the best value for shareholders will be achieved by retaining the business," the company said.
Aviva also said it would keep its joint venture business in China.
The company added, however, that it was looking at strategic options for its operations in Vietnam, Indonesia and Hong Kong, where recent pro-democracy protests have threatened the territory's position as one of Asia's major financial centres.
Aviva's structure is considered clunky by analysts and investors, who expect Tulloch to unveil a streamlining of operations at the firm's investor day this week.
Sources familiar with the divestment plans told Reuters that very few bidders were interested in the Singapore business given the price tag and also as most global and regional insurers have an existing presence in Singapore.
Aviva's decision to keep the business "would lead you to believe ... it isn’t worth what they think it is," one trader told Reuters.
Reuters reported in September that Aviva was hoping to sell the Singapore and Vietnam businesses, its only wholly owned businesses in Asia, for up to $2.5 billion.
Bloomberg reported earlier on Monday that Japan's MS&AD Insurance Group Holdings and Canada's Manulife Financial were looking to buy Aviva's assets in Singapore and Vietnam.
Shares in the FTSE 100 company fell to two-week lows after the Aviva announcement, and were down 3.6% at the bottom of the index by 0938 GMT. The absence of a sale would make it harder for Aviva to pay down debt or give capital back to shareholders, which would likely be "disappointing for investors", said Shore Capital analysts, reiterating their hold rating on the stock.
Aviva's Asian businesses are in China, Hong Kong, India, Indonesia, Singapore and Vietnam.
The Asian operations posted a 25% rise in operating profit to 284 million pounds in 2018, according to Aviva's annual report. Singapore contributed nearly half of the Asian businesses' operating profit.
By Muvija M and Carolyn Cohn