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.
Both Apple and Google declined to 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.
In addition, the companies are both major rivals of software giant Microsoft Corp.
Separately, the U.S. Justice Department is also making inquiries about a class action settlement that Google reached giving it the right to digitize and sell entire libraries, according to experts on digitization.
Last week, U.S. President Barack Obama appointed Schmidt to the President's Council of Advisors on Science and Technology, a 20-member group that will help formulate policy on areas where understanding of science and technology is important.
(Reporting by Gabriel Madway and Alexei Oreskovic; Editing by Richard Chang)