Alisson Becker could be missing for up to two months after suffering a calf injury during Liverpool's opening Premier League game on Friday.
The goalkeeper is set to miss Liverpool's 2019 UEFA Super Cup match against Chelsea on Wednesday in Istanbul, Turkey.
New signing Adrian replaced the 26-year-old against the Canaries, making his debut after joining the club on a free transfer on Monday.
The former West Ham United 'keeper should be set for a run in the starting XI, with free agent Andy Lonergan potentially deputising for Adrian on the bench.
Per Connor Dunn of the Liverpool Echo, Lonergan could be offered a short-term deal to cover while Alisson recovers.
Simon Mignolet recently left the club to sign for Club Brugge, depleting Jurgen Klopp's senior options on Merseyside.