The portfolio, known as Galaxy Project and worth 10.8 billion euros ($12.81 billion), also includes the disposal of Alpha's bad loan servicing unit, Cepal.
Davidson Kempner has valued the assets at about 290 million euros, trumping a rival offer by U.S. investment giant Pacific Investment Management Company (PIMCO), one of the sources said.
Alpha Bank declined to comment while Davidson Kempner and PIMCO were not immediately available.
The sale, which is expected to be finalised by the end of 2020, is the most significant attempt by a Greek bank to clean up its balance sheet amid fears that the proportion of soured loans to businesses and individuals will surge as a consequence of the COVID-19 crisis.
Greece has the highest bad-loans ratio in the European Union.
Banks offload bad debts, normally at a fraction of their face value, to free up their balance sheets to make new loans and keep both their own business and economies going.
The sale of the Galaxy portfolio is expected to reduce Alpha's non-performing exposure (NPE) ratio to 24% from around 43% and its non-performing loan (NPL) ratio down to 13% from 30%, a banking source familiar with the deal said.
Alpha launched the process early this year, drawing initial interest from a series of bidders including Italian firms Cerved and Credito Fondiario, the sources said.
But only Davidson Kempner and PIMCO made binding offers and advanced to the final stages of the auction, with Alpha's board selecting Davidson Kempner as its preferred bidder after a board meeting on Friday.
Cepal, with a headcount of about 900, will be servicing the portfolio of bad loans that Davidson Kempner is expected to buy, in addition to non-performing loans of other parties. It currently services a little under 30 billion euros of impaired loans.
Alpha Bank, which initially held only 40% of Cepal, took full control of the platform in July from Centerbridge.
"Cepal is the main prize for this deal as the new owner will be entitled to the annual servicing fees that Cepal generates," one of the sources said.
Another source said Davidson Kempner's bid came with an attractive earn-out scheme and limited contractual protections.
The decision to negotiate a deal with Davidson Kempner could be announced early next week, the sources said.
It follows a similar transaction by Greece's Eurobank to sell 80% of its loan servicing unit FPS to Italian debt recovery firm doValue along with a chunk of mezzanine and junior notes from a 7.5 billion euro bad loan securitization known as Project Cairo.
Alpha Bank has applied to fold Galaxy into a Greek government scheme, dubbed Hercules, which provides state guarantees on the senior tranches of the securitisation.
(Reporting by Pamela Barbaglia in London and George Georgiopoulos in Athens; Editing by Diane Craft and Matthew Lewis)
By Pamela Barbaglia and George Georgiopoulos