Having assessed the bids received as part of the sales process, with the assistance of its advisers, the company said in a sales process update that it will enter discussions with an affiliate of Henderson Park Capital Partners
The firm, which became Ireland's first REIT when it joined the stock market in 2013, announced the sale in April because shareholders were stuck with a "material and persistent" discount between its share price and the value of its portfolio.
The company did not reveal the identity of the other bidders, but Great-West Lifeco owned Irish Life and Kennedy Wilson were in the running, the Sunday Times reported.
Other parties linked to the bidding include Canadian investment group Brookfield, which has wind farm and telecoms interests in Ireland and German funds, including Union Investment, part of the DZ Bank group, the newspaper added.
Green REIT is looking to either sell the entire company or its 1.5 billion euro portfolio of assets which are focused on commercial property in the Dublin area with tenants including Barclays, Allied Irish Banks, Bank of America and WeWork.
JPMorgan Cazenove is the lead adviser on the deal, Davy is joint adviser.
The company said the completion of any offer would be subject to customary conditions for an offer for an Irish public company and there is no certainty a firm offer will be made.
(Reporting by Graham Fahy; editing by David Evans)