Australia's newest professional outfit are currently 13th in the Super Rugby standings and bottom of the Australian Conference having lost five matches on the bounce.
Hill is under contract until the end of the season but chief executive Steve Boland has suggested that changes may be made far sooner if improvements aren't forthcoming.
"We've had some discussions with Damien," said Boland.
"The coaching window and player recruitment window can't wait until the end of the season for those sorts of decisions so we need to make a decision on our coach well before the end of the year.
"We're all in the same boat. We need to see some performances that justify the team we've got and the effort everybody's putting in."
The Rebels' only win came in their season opener at home to the Force on February 15 and they have since slipped to defeats to the Brumbies, Reds, Waratahs, Sharks and Cheetahs.
Hill's team have conceded more points than any other Super Rugby side and have scored the joint-lowest despite boasting a playing rooster that includes the likes of James O'Connor, Kurtley Beale and Scott Higginbotham.
The Rebels' problems haven't been limited to on-field disappointments either, with frustrations boiling over off-the-field after the record 64-7 loss to the Sharks in Durban a week-and-a-half ago.
Beale and Wallaby wing Cooper Vuna were sent home from the tour of South Africa after being involved in an altercation on the team bus as the squad returned from a night out.
Both men faced disciplinary procedures and Beale has been stood down indefinitely by the Australian Rugby Football Union and told to seek external counseling after it emerged that he punched club captain Gareth Delve.