By Sam Oliver

Published: 07:55 PM EST

Following the departure of Google executive Eric Schmidt from the Apple Board of Directors, the company's governing body will reportedly convene next Tuesday to ponder a replacement.

The news comes from a source familiar with the matter who spoke with The Wall Street Journal. It would be a special meeting for the board, which typically only meets four times a year.

Schmidt resigned recently resigned from the Apple board, citing a conflict of interest as his own company ventures into the smartphone market with Android, and soon the PC operating system world with the upcoming Chrome OS. His presence with both companies had already sparked a Federal Trade Commission investigation -- one that remains ongoing because Arthur Levinson, former CEO of Genentech, also serves on the boards.

Since the Google chief's departure, speculation has arisen as to who might replace his seat. Many have pointed, as the Journal's report did, to Apple Chief Operating Officer Tim Cook. He has held that position since October of 2005.

In the wake of Schmidt's departure, it was revealed that Google and Apple shared an agreement to not poach each others' employees, which may have sparked an antitrust investigation from the U.S. Justice Department.

Prior to his resignation, Schmidt already had to recuse himself from board meetings that involved iPhone plans, many of which would clash with Google's own attempts to promote its Android mobile operating system. Though the Google executive was adamant that the two companies don't occupy the same markets, the FTC is still investigating the Apple-Google link for a possible violation of antitrust laws through unfair collaboration.

Tension has also mounted between Google and Apple in recent weeks, as the iPhone-maker rejected the Google Voice application, as well as third-party software that used the free service, from the App Store. That event has since sparked an FCC investigation.