The head of American International Group Inc.’s giant aircraft-leasing business in Los Angeles is in talks to buy a piece of the unit amid growing frustration at AIG’s delay in selling the company.

Steven Udvar-Hazy, chairman and chief executive of International Lease Finance Corp., is in early discussions to purchase about $2 billion of the company’s aircraft portfolio and use it to start a rival business, according to people familiar with the matter. ILFC’s fleet is valued at a little more than $40 billion.

ILFC, one of AIG’s most prized assets, has been on the block for almost a year as part of AIG’s efforts to raise cash to repay government aid. AIG has yet to find a buyer for the company, which is saddled with more than $30 billion in debt. Hazy, who initially had hoped for a quick sale of ILFC, has bristled under AIG’s government stewardship and has complained that AIG’s woes have made it hard for ILFC to gain access to credit markets.

In the spring of 2008, Hazy explored leading a buyout, but the two companies concluded ILFC was worth more as part of AIG.

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