Two years ago, the government injected money into the bank in what is called a contingent capital bond – money that could be used if the bank's reserves fell below a certain level.
But the bank and Department say this morning that international investors have expressed interest in buying out this bond.
Part of the interest is coming from investors who bought into the bank last year.
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It's thought the government may sell a minimum of €500 million and up to a full billion euro worth of its stake.
Our Business Editor Ian Guider has been looking at the figures: