The FTC has already notified the companies of the inquiry the report said, citing people briefed on the matter.
Google Chief Executive Eric Schmidt and former Genentech CEO Arthur Levinson are directors of both companies. Under federal antitrust law, a person is not allowed to sit on the board of two companies if it decreases competition between them.
An Apple spokesman declined to comment. Google officials could not immediately be reached for comment.
The two companies compete directly or indirectly in a number of areas, the most obvious being the fast-growing smartphone market.
Apple's iPhone has been a huge hit for the company and is key to its future growth prospects. Google's Android operating system is used on T-Mobile's G1 smartphone.
(Reporting by Gabriel Madway and Alexei Oreskovic)