The bank, which is owned by Denmark's Danske Bank, closed all its 27 branches in Ireland last month. Its customers here now have to use options such as phone or internet services, post offices or one of a handful of Danske Bank 'advisory centres' to meet staff face-to-face.
Sixteen of the closed branches were in Dublin.
Among the properties put up for sale was a high-profile premises on Dublin's College Green. It has a €4m price tag.
Another former branch was on O'Connell Street in the capital. There's a guide price of €1m on that property.
Stephen McCarthy, an associate at Savills, said there has been significant interest in the properties.
He said interest had principally come from domestic players, but that there had been some enquiries from international clients.
Potential buyers were happy to meet asking prices, he said.
"This isn't a distressed sale." Mr McCarthy said that interest was particularly strong for the premises that are located in urban areas and that a range of potential buyers were in the mix.
Danske Bank has denied that the closure of its branch network marks another step towards eventually pulling out of Ireland.
In the first half of this year, NIB recorded a €401m loss and made a further €391m provision for loan impairment charges.
That impairment charge was down from the €401m it set aside in the first half of 2011.