NEW YORK (Reuters) - AIG is soliciting bids for International Lease Finance Corp after a group led by the unit's chief offered to buy a small portion of the aircraft lessor's fleet, according to sources familiar with the matter.

American International Group Inc has reached out to potential bidders, including those that showed interest in the unit earlier, the sources said. These include Carlyle Group , Terra Firma Capital Partners Ltd and TPG , one of the sources said.

The federal government, which owns nearly 80 percent of AIG and has pledged some $180 billion to prop up the insurer, would prefer to sell part of ILFC, not just the fleet, because it does not want to get stuck with "undesirable assets" it might not be able to sell, the source said.

The solicitation process is a result of those concerns, the source said.

A second source said the effort was more akin to a buyout situation, where the board solicits other interest after getting an offer from management.

At a time when funding remains hard to come by, Credit Suisse is offering about $2 billion in financing to the ultimate buyer, the sources said.

One of the sources said the amount of financing could be larger, depending on how big a stake is sold.

More clarity on where things stand is expected in the next seven to 10 days, although a deal could still be weeks away, the sources said.

A group led by ILFC chief executive Steven Udvar-Hazy has offered to buy about 10 percent of the unit's aircraft portfolio for roughly $4 billion, the sources said.

Udvar-Hazy is backed by a group that includes private equity firms Onex Corp and Greenbriar Equity Group.

Udvar-Hazy effectively invented the business of plane leasing when he started ILFC in 1973. The benefits of leasing rather than buying planes appealed to start-ups and traditional airlines alike, and he built up and sold the company to AIG in 1990 for about $1.3 billion.

ILFC has a portfolio of about 1,000 aircraft, with a book value of more than $40 billion.

Carlyle, declined to comment. Representatives for TPG and Terra Firma did not have immediate comment. AIG was not immediately available for comment. The sources are anonymous because talks are not public.

AIG has been trying to sell Los Angeles-based ILFC for about a year as part of its efforts to pay back the US government, but many internal deadlines have passed without a deal.

A sale has proved to be a challenge due to the lessor's mountain of debt and funding needs. ILFC had roughly $30 billion of total debt financing and subordinated debt as of September 30.

The process was also slowed after AIG appointed a new chief executive, Robert Benmosche, this summer, its fourth since June of last year. Benmosche is overseeing a broad restructuring and trying to pay back some $61 billion of US taxpayer funds that AIG still owes.

Selling a part of the aircraft lessor, which is one of the biggest customers of Boeing Co and Airbus, would make only a small dent in the insurer's outstanding bill.

AIG's shares were up 23 cents or one percent at $30.12 on the New York Stock Exchange on Friday.