The goalkeeper and newly signed midfielder have not been able to feature in the workouts at Melwood in preparation for the Anfield showdown, with the nature and extent of their issues still unknown.
Liverpool have a late session on Sunday and even if the pair are able to join the group for it, they will still require assessments on Monday before being considered for selection by Jurgen Klopp.
Alisson suffered hip and calf problems last season, rendering him unavailable for 14 matches.
Thiago has been in line to make his full debut after a hugely impressive cameo in the centre of the park in the 2-0 victory over Chelsea at Stamford Bridge.
Klopp is still without captain Jordan Henderson and Joel Matip, both nursing muscle problems, but Joe Gomez returned to training on Friday.
Liverpool are unbeaten in their last 60 Premier League home games, while Arsenal are looking to win their opening three matches in the division for the first time since 2004-05.
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