The buyout firms made bids two weeks ago for GE Capital Commercial Distribution Finance, a unit with $11 billion in assets, the report said, citing people familiar with the matter.
Bloomberg said GE could select a buyer for the unit by the end of the month.
GE said in April it would seek to sell some $200 billion of its GE Capital assets as it moves away from financial services and focuses more on manufacturing jet engines, power turbines and other big-ticket industrial equipment.
KKR did not immediately comment, while Apollo declined comment. GE could not be immediately reached for comment.
Reporting by Sruthi Shankar in Bengaluru; Editing by Savio D'Souza