The 18-year-old was stretchered from the field at Elland Road after sustaining the injury in a challenge midway through the second half.
Elliott will be required to undergo surgery in the coming days and the club will offer a further update on his prognosis in due course.
Harvey, his family and Liverpool FC would like to place on record their thanks to the paramedics and all the staff at Leeds General Infirmary for the care and treatment given.