NEW YORK - Standard & Poor's said on Tuesday it is continuing to review its ratings on International Lease Finance Corp for downgrade as American International Group Inc's plans to sell the unit have become less clear.

S&P has ILFC on review for downgrade from BBB-plus, the third lowest investment grade.

AIG and Steven Udvar-Hazy, head of ILFC, the world's largest plane leasing firm, are weighing several options for the business, including breaking up the company, two sources familiar with the matter said on Saturday.

The company, one of the biggest customers of Boeing Co and Airbus has been on the block since late last year after its parent's near-collapse.

We believe that if AIG is re-evaluating a potential sale of ILFC, it could lessen the near-term likelihood of the worst outcome for creditors, specifically the sale of ILFC on terms that leave it unable to access debt markets to refinance substantial near-term maturities, S&P said in a statement.

However, alternatives to a near-term sale carry risks, including the possibility that senior management, including Udvar-Hazy, could leave and form a new company, S&P said.

Also, if most or all of the assets and operations that support ILFC's rated debt remain with AIG, Standard & Poor's would re-evaluate whether the aircraft lessor's stand-alone credit profile, plus credit for potential parental support, still justify our current ratings, S&P said.

The cost to insure ILFC's debt has jumped on increased uncertainty about the company's future.

Credit default swaps on ILFC's debt increased to around 18 percent of the sum insured as an upfront cost on Tuesday, or $1.8 million to insure $10 million for five years, plus $500 million per year, from 13.75 percent on Friday, according to data by Markit Intraday.

(Reporting by Karen Brettell; editing by Jeffrey Benkoe)