Google has attracted the attention of anti-trust regulators in recent weeks
The Federal Trade Commission is looking into the ties between the boards of Apple and Google, according to reports.
The New York Times said the inquiry involving Google and Apple centres on a possible breach of anti-trust laws.
Google boss Eric Schmidt and former Genentech boss Arthur Levinson sit on the boards of both companies.
The Clayton Anti-trust Act of 1914 forbids a person to be on a board of two rival firms at once if it reduces competition between them.
Apple and Google both offer competing web browsers and phone operating systems. However they have worked together, most recently to design versions of some of Google's services like Gmail and Google Maps for the iPhone.
Legal experts say the issue is rarely pursued partly because it is difficult to prove how overlapping directors impinge on business decisions.
"Government actions under Section 8 are rare, but they are brought under circumstances when the presence of a common director on competing boards is likely to be anticompetitive, " Andrew I. Gavil from the Howard University School of Law told the New York Times.
One easy solution to the problem would be for either director to step down from one of the two boards.
Google, Apple and the FTC have all refused to comment on the report.
This is the second anti-trust inquiry to involve Google in recent days.
Last week the Department of Justice started its own investigation into the company's $125m (£82.7m) settlement with authors and publishers to digitise millions of books and make them available online.
Despite competing products Google and Apple have also worked together
Christine Varney, the assistant attorney general for the Justice Department's anti-trust division has said that she is concerned about Google's power, particularly in the online advertising space.
Comments she made at an earlier panel discussion sponsored by the American Anti-trust Institute were resurrected when she was nominated to be the US's next anti-trust chief.
"For me, Microsoft is so last century. They are not the problem," Ms Varney said at the time.
Last week, Google's Mr Schmidt was appointed to President Obama's Council of Advisors on Science and Technology, a 20-member group that will help formulate policy in a number of areas "where understanding of science, technology and innovations is key to strengthening the economy".