American International Group Inc has picked a group that includes private equity firms Onex Corp and Greenbriar Equity Group as the preferred bidder for its aircraft leasing unit, a source familiar with the situation said on Friday.

The insurer has, however, not signed an exclusivity agreement with the group for International Lease Finance Corp, the source said.

The consortium wants to keep the aircraft leasing business intact, the source said.

Spokespersons for AIG, Onex and Greenbriar were not immediately available for comment.

The planned sale is part of a larger divestiture program by AIG, as it looks to pay back the U.S. government after a massive bailout. The government has committed some $180 billion to AIG's rescue, including about $85 billion in loans.

ILFC had total debt financing and subordinated debt of about $32 billion as of March 31, some of which starts to mature in October.

Other groups bidding for ILFC have included private equity firms Thomas H. Lee Partners and Carlyle Group [CYL.UL] and Terra Firma Capital Partners Ltd [TERA.UL], sources have told Reuters.

As of March 31, ILFC owned 972 aircraft in its leased fleet.

AIG's shares were up 4.88 percent, or 8 cents, changing hands for $1.72 in midafternoon trading Friday on the New York Stock Exchange. (Reporting by Paritosh Bansal, additional reporting by Phil Wahba, editing by Gerald E. McCormick) (For more M&A news and our DealZone blog, go to www.reuters.com/deals)