The former No. 2 to Twitter fan Rupert Murdoch is one of the top choices among the people being interviewed for the part-time gig, All Things D reports. But the site says it hears from unnamed sources that Twitter management is just beginning its search, and Peter Chernin is still mulling whether he even wants the job. The privately held company — believed to be a prime candidate to go public once it solidifies its business model — has a seat to fill in the board room following the recent departure of  Flipboard’s Mike McCue. (He’s said to be concerned that his company might soon compete with Twitter.) Chernin has strong credentials: At News Corp he was one of the architects of Hulu. Since he left, his Chernin Entertainment has been a prolific developer of TV shows (including Fox’ New Girl) and movies (such as Fox’ Rise Of The Planet Of The Apes).