* First visit by top Saudi oil official to Iraq in 30 years
* Iraq has so far insisted on extending OPEC cuts by 6 months
* Saudis want OPEC cuts to be extended by 9 months
* Goldman says stocks should normalise if cuts are prolonged (Updates with OPEC SecGen, Goldman)
BAGHDAD/VIENNA, May 22 (Reuters) - Saudi energy minister Khalid al-Falih paid a rare visit to Iraq on Monday in the latest effort by the top oil producer to convince its fellow OPEC member to extend supply cuts for a further nine months to ease the global glut and prop up prices.
The Organization of the Petroleum Exporting Countries will meet in Vienna on Thursday to consider whether to extend curbs agreed in December last year between OPEC and 11 non-member countries, including Russia. The existing cuts run until June.
Saudi Arabia and non-OPEC Russia have been pushing to extend the cuts by nine months until March 2018. Iraq, OPEC's second largest and fastest growing oil producer, has so far voiced support only for a six-month extension.
It is the first time in nearly three decades that a senior Saudi energy official has visited Baghdad.
"The two ministers will discuss boosting bilateral relations and the upcoming OPEC decision to help boost global prices and reduce the glut in the market," Iraqi oil ministry spokesman Asim Jihad told Reuters.
The two ministers were expected to hold a news conference later on Monday after the talks.
OPEC wants to reduce global oil inventories to their five-year average but so far has struggled to do so. Stockpiles are hovering near record highs, partly because of rising production in the United States, which is not part of the existing deal.
"I believe we have a growing consensus (on the duration of cut extension)," OPEC's Secretary General Mohammad Barkindo told reporters in Vienna.
Iraq and Iran were the main stumbling blocks for OPEC in reaching its last output-cutting decision in December.
Baghdad argued it had just started enjoying production growth after years of stagnation and Tehran said it needed to raise output after the lifting of Western sanctions.
Iraq ended up by agreeing to cap output in the first half of 2017 while Iran was allowed a slight rise in production as part of the deal by OPEC and non-OPEC states to curb output by about 1.8 million barrels per day or 2 percent of global extraction.
Nigeria and Libya were granted exemptions from the cuts as their output suffered from unrest. Both have regained some volumes in recent months and are expected to add more soon, adding to OPEC's challenge in rebalancing the market.
Goldman Sachs, one of the most active banks in commodities trading, said on Monday a nine-month cut extension would help rebalance inventories in 2017 and keep Brent prices near $57 per barrel.
Brent futures traded 1 percent up around $54 a barrel on Monday at 1455 GMT.
Goldman said OPEC should work to intimidate American shale oil producers by creating a market structure known as backwardation, when the future trading price of a commodity is below the current spot market value.
By extending cuts into 2018 and promising to boost output next year, OPEC could force the oil market into backwardation that would scare away private equity and other investors who have been funding American shale producers.
"The binding force to sustainably slow shale growth lies on the funding side," Damien Courvalin, a Goldman analyst, wrote in the research note to clients. (Additional reporting by OPEC team in Vienna; Writing by Isabel Coles and Dmitry Zhdannikov; Editing by David Goodman and Edmund Blair)