(Adds OPEC+ deliberations in paragraphs 21-23)

DUBAI, May 31 (Reuters) - Saudi Arabia and its bankers on Sunday will start taking orders for as much as $13.1 billion worth of shares in its energy giant Aramco, in a major test of international investor interest in its market.

In a long-anticipated announcement on Thursday, the kingdom and Aramco detailed plans to sell up to a 0.7% in the state-controlled oil company, with 10% of the offering reserved for retail investors, based on demand. Order-taking will run through June 6 and the deal will price on June 7.

The offering - codenamed Project Bond according to sources - has been trailed for months as a key step in drawing a broader range of investors after Aramco's record-breaking initial public offering (IPO) in 2019. The move will also further the kingdom's massive economic diversification programme.

The deal will be a test of interest in Saudi markets after lukewarm demand from international investors for the IPO amid concerns about a high valuation, Saudi government control and the energy transition away from hydrocarbons.

International investors have been similarly reticent about the kingdom's mega-projects, from beach resorts to new cities.

Investors buying into Aramco will need to weigh environmental concerns against its rich payouts.

"Since the IPO, higher expectations on dividend payout and oil price have outweighed lower expectations on output," said Hasnain Malik, head of equity research, at Dubai-based Tellimer.

"That improvement in the cash flow available for shareholders may not be enough to entice those foreign investors that did not participate in the IPO because of environmental concern on fossil fuels or governance concern on the priorities of the dominant sovereign shareholder."

When asked about whether there had been any interest from so-called anchor investors to take a major chunk of the offering, Aramco Chief Financial Officer Ziad Al-Murshed gave little away.

He noted the shares are on sale above the IPO price - within a range of 26.7 riyals ($7.12) to 29 riyals, after they closed at 29.1 riyals on Thursday, valuing the company at $1.87 trillion. Aramco's IPO valued it at $1.7 trillion.

The sale comes as stock offerings globally have reached $247.4 billion in the year to date, the highest level since 2021, according to Dealogic data. It will be one of the biggest share sales in the last decade.

'SELF-FUNDING'

Saudi Arabia's de facto ruler Crown Prince Mohammed bin Salman, known as MbS, has poured hundreds of billions of dollars through the kingdom's sovereign Public Investment Fund (PIF) into massive projects, and everything from electric vehicles to sports and a new airline, to diversify the economy away from hydrocarbons and create jobs.

Selling Aramco shares is "not the only way to fund (MbS') Vision 2030, but it's one of the easier options now that it's clear foreign investors aren't interested in buying stakes in Saudi gigaprojects," said Jim Krane Research fellow, Rice University's Baker Institute Houston.

"The Saudis have not been able to attract enough foreign investment to cover much of the cost of building the Vision 2030 gigaprojects, like the massive beach resorts and futuristic cities. It's not for lack of trying."

Krane expects most of the buyers of the offering will be Saudis. "So, it's an indirect form of self-funding by Saudi investors who receive shares of Saudi Aramco instead of a piece of Neom or the New Murabba," he said, referring to two of the mammoth projects being spearheaded by the PIF.

Selling on the Saudi Exchange also offers lighter regulatory and transparency requirements, he added.

The kingdom is supported by a familiar phalanx of advisers, as for the Aramco IPO. Wall Street dealmaker Michael Klein's firm Klein & Co and U.S. boutique firm Moelis & Co are acting as independent advisers on the deal, according to a filing with the Saudi Exchange Thursday.

Saudi National Bank's investment banking arm SNB Capital is acting as lead manager in addition to its role as joint global coordinator alongside Morgan Stanley, Citi, Goldman Sachs, HSBC, Bank of America and JPMorgan.

Aramco CEO Amin Nasser told reporters the sale was an opportunity for current and new investors to build a sizeable position in the company, and for Aramco to broaden its shareholder base and boost the liquidity of its shares.

Saudi Arabia is the de facto leader of the Organization of the Petroleum Exporting Countries, which - via the OPEC+ group with allies such as Russia - helps to engineer price moves on world oil markets.

The share sale coincides with a meeting of OPEC+ on Sunday to decide its next production policies. The group is seeking ways to extend some of its deep oil production cuts into 2025, sources familiar with the discussions have told Reuters.

A rollover is increasingly expected by markets and "may not result in as much of a boost to prices," said James Swanston of Capital Economics

($1 = 3.7506 riyals) (Reporting by Maha El Dahan, Hadeel Al-Sayegh and Yousef Saba. Writing by Anousha Sakoui. Additional reporting by Saeed Azhar and Karin Strohecker. Editing by Mark Potter)