By Lefteris Papadimas and Angeliki Koutantou

ATHENS (Reuters) -The sale of a 27% stake in Piraeus Bank by Greece's bank bailout fund (HFSF), worth about 1.3 billion euros ($1.41 billion), was oversubscribed by more than three times on Monday, sources close to the process told Reuters.

Greece's third largest lender will be the third of the country's four big banks to be fully privatised since last autumn after the Greek economy was raised to investment grade.

Interest in the Piraeus sale, which was announced on Sunday, is a positive sign for the Greek economy after a decade-long debt crisis that saw the Mediterranean country nearly fall out of the euro before receiving three international bailouts.

HFSF said it had decided to sell the entire 27% stake due to strong demand, confirming an earlier Reuters report.

"The offering has been oversubscribed in a few minutes after the books opened," the first source said, adding that up to 25% will be offered to institutions and 2% to retail investors.

A few hours later, two sources said that the Piraeus stake sale, which will run until Wednesday, was more than three times oversubscribed.

The initial price range was set between 3.7 and 4 euros per share, the state-controlled HFSF said late on Sunday.

"The majority of the bids from investors are in the upper part of the price range," the first source added.

Shares in Piraeus, which has a market value of around 4.98 billion euros, were up 4.18% to 4.19 euros at 1314 GMT.

After injecting about 50 billion euros to prop up Greece's four largest banks in return for shares during the debt crisis which ended in 2018, HFSF began divesting its stakes last year.

It divested its holdings in Eurobank and Alpha Bank and sold part of its stake in National Bank last autumn.

BofA Securities, Goldman Sachs Bank and UBS are acting as joint coordinators for the offering of Piraeus stake.

($1 = 0.9223 euros)

(Reporting by Lefteris Papadimas and Angeliki Koutantou; Editing by Edward McAllister, David Evans and Alexander Smith)