Mr Ban's term as head of the global body is due to expire at the end of 2011 Mr Ban has won praise for championing the issues of climate change and women's rights, but his low-key style has drawn some criticism.
Diplomats say that with no rival for the position, he could win a vote before the end of the month.
Mr Ban said he had sent a letter to UN member states to "offer, humbly, myself in consideration for a second term as secretary general of the United Nations".
His term is due to expire at the end of the year.
Analysts say that if he is unopposed, the UN Security Council could give its approval and the UN General Assembly hold a vote on the role before the end of June.
Mr Ban's office has defended his approach to international diplomacy, saying he works behind the scenes with quiet diplomacy as well as public pressure to promote human rights.
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