The 17-year-old forward suffered a heavy fall during the young Reds' 3-2 Premier League 2 defeat and left the field on a stretcher.
Following an initial diagnosis of ligament damage, Brewster will undergo further tests this week to determine the full extent of his injury.
Brewster has been a regular fixture for Neil Critchley’s U23s this season, as well as the club’s U19s in the UEFA Youth League - a side managed by Gerrard.
Speaking to Liverpoolfc.com, Gerrard said: "Rhian is a great kid and a fantastic footballer. He is a mentally strong kid as well and I’m sure he will bounce back.