WASHINGTON, July 13 (Reuters) - A key bank regulator has been "very reluctant" to provide relief to troubled lender CIT Group CIT.N through a government debt guarantee program, a source familiar with the matter said on Monday.

The source said the Federal Deposit Insurance Corp has been cool to the idea of granting CIT access to its debt guarantee program, partly because the regulator is not satisfied with the lender's collateral, even though the Treasury Department and Federal Reserve have been more supportive of such a move.

The Treasury and Fed are exploring other ways to provide relief to the New York-based commercial lender, including possibly granting CIT's request to transfer assets to its CIT Bank unit, the source said, speaking anonymously because the government discussions have been private. (Reporting by Karey Wutkowski; Editing by Phil Berlowitz)