According to a report in The Wall Street Journal citing a source familiar with the matter, the Apple directors have scheduled a meeting, although the company will not respond to requests to confirm the report.
Schmidt stepped down from the Apple board because regulators had expressed concerns that the two companies could be colluding, especially since Google is now making phone software.
However, Schmidt's departure was not enough for the Federal Trade Commission, which will continue to scrutinise the relationship between the two companies and the remaining interlocking directorates.
Genentech chairman Arthur Levinson, who joined the boards of Apple in 2000 and Google in 2004, is the remaining person serving on the boards of the two competing companies.
It is unclear whether the Tuesday meeting will also discuss Levinson's position on the board.
Apple's directors meet at least four times a year, according to the governance guidelines on Apple's web site.
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