American International Group Inc. may raise its stake in Asian insurer AIA Group someday and is open to offers for its airplane leasing business ILFC, but will bide its time on all these things, Chief Executive Bob Benmosche said on Wednesday.

Benmosche, speaking at a Bank of America Merrill Lynch insurance conference, made clear that AIG was in no rush to make any decisions on key assets. The company, bailed out by the U.S. government in late 2008, is still 77 percent owned by the Treasury Department.

As part of its efforts to repay that bailout, it took AIA public in Hong Kong in 2010 but retained a one-third stake. When AIA shares rise that creates substantial profits for AIG, but when the stock falls it generates major losses.

Benmosche said one option might be to someday raise AIG’s stake in AIA to 51 percent. Before that, though, AIG will have to pay off the government’s preferred interest in the entity that holds the AIA shares.

Proceeds from a sale of ILFC are expected to go toward that goal. AIG filed for an initial public offering for ILFC last fall but has done little since. Benmosche said the time for an IPO was not right, given “noise” in the aviation market. But he added he would listen to reasonable offers for the unit.

He made clear that one asset not going anywhere is United Guaranty, or UGC, the company’s mortgage insurance business. At one time UGC was seen as a non-core asset that might be sold to raise capital. But as competitors have struggled, UGC has become the largest mortgage insurer in the country.

Benmosche described UGC as a core asset on Wednesday and said it gave AIG valuable insight into the mortgage market.