ATHENS, Jan 15 (Reuters) - Greece's bank bailout fund will start a process to sell a stake in Piraeus Bank, the country's third largest lender, by March, two sources familiar with the matter told Reuters on Monday.

It's the third such sale since October from the state- controlled Hellenic Financial Stability Fund (HFSF), which was set up to recapitalise Greek banks during the country's decade-long financial crisis which ended in 2018.

HFSF holds 27% in Piraeus Bank, with a market value of 4.37 billion euros ($4.79 billion), and has yet to decide whether to sell all or part of its shareholding.

"The plan is for the sale to take place at the end of February or early March," a banker with knowledge of the matter told Reuters.

"There is no final decision yet on the stake. It might be 17%-18% or the whole stake," he added.

A second source involved in the process said that it would likely be a combined sale to retail and institutional investors.

HFSF has mandated BofA as an advisor on its stake.

After injecting about 50 billion euros into the sector, HFSF started reducing its participation in four major Greek banks last autumn as part of its divestment from the lenders which have been recovering.

Greek banks are expected to post strong profits for 2023 and 2024 and hope to start paying dividends in 2024 for the first time since 2010, when the Greek debt crisis erupted.

Greek bank shares have gained 7% since the start of the year after a 67% jump in 2023, benefiting from the country's strong growth and its recent credit rating upgrade to investment grade.

HFSF sold a 20% stake in National Bank and a 9.4% stake in Alpha Bank in November.

($1 = 0.9122 euros) (Reporting by Lefteris Papadimas, additional reporting Renee Maltezou; Editing by Emelia Sithole-Matarise)