The firm, which became Ireland's first REIT when it joined the stock market in 2013, made the surprise announcement after it said shareholders were stuck with a "material and persistent" discount between its share price and the value of its portfolio.
Great-West Lifeco owned Irish Life and Kennedy Wilson remain in the running, the Sunday Times said.
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. J.P. Morgan Cazenove is the lead adviser on the deal.
A spokesman for Green REIT said the company is not commenting on any aspect of the sales process.
(Reporting by Padraic Halpin; Editing by Raissa Kasolowsky)