* Sale could raise $30 billion, help pay for oil spill
* Possible route for Rosneft to become global oil giant
* Sale would cut BP output 30 percent, $2-4 bln/yr in dividends
* BP shares jump
LONDON/MOSCOW, June 1 (Reuters) - A Russian state firm has offered to buy BP's half share in its huge oil joint venture, a source said on Friday, in what would amount to a stunning reversal for the British firm and a bold assertion of Kremlin control over the oil sector.
If a state firm acquires the stake, that would signal a dramatic reorganisation of Russia's oil industry - the world's largest - just weeks after Vladimir Putin returned to the presidency.
Selling out would see BP abandon nearly a third of its oil production after years of maintaining that its giant investment in Russia was a cornerstone of its strategy.
But it would also cut it loose from hostile partners, raise around $30 billion and free it from an investment that had restricted its ability to pursue other opportunities in Russia.
BP did not say who had made the "unsolicited approaches" to buy the giant stake, but a source close to the matter said one of the Russian state-owned oil and gas firms was involved.
TNK-BP is Russia's third largest oil producer, and BP's stake represents one of the biggest foreign investments ever made in the country. It has earned BP huge profits but has long been plagued by acrimonious legal battles between BP and its Russian partners, the AAR consortium of billionaires.
Putin, who returned to the presidency he occupied from 2000-2008, has long discouraged foreign companies owning strategic assets, which limited BP-TNK's ability to expand.
For BP, selling out would mean giving up annual dividends which hit $3.7 billion last year and losing around 30 percent of its oil and gas production, but would give it a cash pile to explore higher-growth ventures, perhaps even in Russia.
Funds raised would help to fund the ongoing cost of cleaning up the 2010 Gulf of Mexico oil spill.
Given the Kremlin's desire to exert influence over the oil sector, analysts and bankers immediately pointed towards state-backed players, especially Rosneft, as the most likely buyers.
"We believe that the eventual buyer will have to be Russia - a 2 million barrels per day company (1 million barrels per day net to BP) is just too strategic for Russia to let fall into foreign hands," said Oswald Clint, oil analyst at Bernstein.
A source close to Rosneft denied it was behind the bid. Another possible bidder could be Rosneftegaz, a state holding company that controls Rosneft.
Last week, powerful former deputy prime minister Igor Sechin was appointed chief executive of Rosneft with - a source close to the group said - a goal to transform the company into a national champion capable of competing on a global scale.
AAR said it had received notice from BP of intent to sell the stake, and repeated its own longstanding offer to increase its holdings.
BP's relationship with AAR is governed by a complex shareholders' agreement, but analysts said this was unlikely to hinder a BP sale. BP said any deal would comply with it.
Investors welcomed the potential sale and shares in BP traded up more than 2.6 percent at 405.3 pence at 1155 GMT.
"BP should exit and reinvest in more profitable areas with less political risk, if it can achieve something close to fair value for the stake," Iain Reid, oil analyst at Jefferies, said.
The proposed sale is an admission that attempts to reach an accommodation with AAR had failed, and BP is effectively throwing in the towel on what was once a core asset.
"We've worked hard to come up with a solution but haven't been able to do so," a source close to the situation said.
BP and AAR have had disputes almost since the creation of TNK-BP in 2003. In 2008, BP Chief Executive Bob Dudley, then CEO of TNK-BP, was forced to flee Russia under what he described as a campaign of harassment from AAR.
Last year, tension flared when BP signed an Arctic exploration deal with Rosneft. An arbitrator ruled that deal was in contravention of the shareholder agreement, under which BP was barred from dealings in Russia outside the joint venture.
BP offered to buy AAR out for around $32 billion, with a plan to subsequently sell the stake on to Rosneft, to settle the spat, BP sources said at the time. But the deal fell apart and the two partners landed in court.
On Monday, one of the AAR billionaires, Mikhail Fridman, resigned as chief executive of TNK-BP , citing a breakdown in relations with BP.
BP sources said they believed the resignation was a tactic to force BP to buy out AAR's stake. In a newspaper interview published on Thursday, Fridman said he would consider a sale.
Previously, AAR has mooted buying out BP and sources close to AAR have said they would be prepared to pay $25 billion for the stake.
Valery Nesterov, oil analyst at Troika Dialog, estimated the value of BP's 50 percent stake in TNK-BP at "at least $30 billion", while Denis Borisov, oil analyst at Nomos Bank said a price of around $25 billion was more likely.
BP invested almost $8 billion in cash, shares and assets to form TNK-BP with AAR in 2003 to expand into Russia, one of the few major resource-holders where foreign oil companies could invest at the time. It has yielded BP $19 billion in dividends in total - on average around 10 percent of BP's annual profits - in spite of high Russian taxes on oil production.
Shortly after the venture was formed, Russia became more hostile to foreign and private-sector investment. The Kremlin's preference to reserve larger fields for state-controlled groups has limited TNK-BP's ability to expand.
Although BP said it received more than one approach, it is hard to imagine private sector bidders attempting to win the stake, especially if the Kremlin wants a state firm to buy it.
However, even state players may have problems bidding. Gas export monopoly Gazprom has big investment obligations and Troika's Nesterov said Rosneft could also struggle to raise the cash needed to buy BP's 50 percent stake.
In recent years, Western oil companies have begun to team up with state-backed players like Rosneft and Gazprom to develop major new fields - often offshore - where growth prospects are greater and the Western firms can contribute expertise.
A sale of the stake would free BP up to expand in Russia without the constraints of the TNK-BP shareholders' agreement.
The strategy of churning low-growth assets to reinject cash into more prospective ventures is one that Dudley has espoused to investors since being appointed in the wake of the oil spill.