The firm, which listed on the Irish stock market in 2013 and focuses on commercial property in the Dublin area, said on Monday the sale process would begin immediately with J.P. Morgan Cazenove as lead financial adviser.
"The company's share price has been subject to a material and persistent structural discount to its net asset value per share for over three years now," Chairman Gary Kennedy said in a statement.
"Following detailed analysis and due consideration, we have decided to focus on the sale of the company or its portfolio of assets."
Green REIT's shares on Monday opened up 5.6 percent at 1.62 euros compared to a net asset value per share of 1.83 euros stated in its year-end accounts.
The company was the first of a wave of real estate investment trusts set up as Ireland's property market began to recover after one of Europe's deepest real estate crashes.
Investec analyst Philip O'Sullivan said both Green REIT and rival Hibernia REIT, had been trading at an "anomalous" discount to book value given Dublin's booming commercial real estate market.
"We have no doubt that there will be ample interest in Green REIT given both the quality of its assets and the strong fundamentals of the Dublin office and logistics markets," O'Sullivan said.
Green REIT's portfolio is 83 percent offices in the Dublin area. Tenants in its buildings include Barclays and Allied Irish Banks.
(Reporting by Conor Humphries; editing by John Stonestreet and Emelia Sithole-Matarise)