The directors at gadget giant Apple are set to meet on Tuesday to discuss who should replace Eric Schmidt on the firm’s board, according to a report in the Wall Street Journal. Schmidt resigned his seat on the Apple board over a conflict of interest with his role of CEO at Google.

The business interests of Google and Apple have increasingly overlapped recently, with Google’s mobile phone operating system Android competing with Apple’s iPhone software and its Chrome web browser and operating system clashing with Apple’s products.

The announcement came shortly after it was reported that the Federal Trade Commission had concerns about Schmidt’s role at Apple, where he had served since 2006. Schmidt’s departure leaves Arthur Levinson as the only other person serving on both Apple’s and Google’s boards.

It is not clear who is in contention to replace Schmidt but the report does say that Tim Cook, currently COO at Apple, may be elected to the board in the not too distant future.

Cook took over the day-to-day running of Apple when CEO Steve Jobs took a six-month medical leave of absence to recover from a hormone imbalance. It was later revealed Jobs had also undergone a liver transplant.