I personally do not think he is regardless of how the season plays out, but this piece on ESPN FC discusses the issue and at least one of the commentators thinks he'll be fired if Liverpool don't win the FA Cup. http://www.espnfc.us/video/espn-fc-tv/86/video/2388227
My take is that he has done a fine job and will be given at least another season. Firing him now would be premature and unless Liverpool have lined up a suitable replacement I just don't see this happening. He and the transfer committee do need to get things right this summer though if Liverpool are going to challenge for top 4 next year.