Chelsea are expected to field a heavily rotated side at Anfield, despite needing a win to keep their faint Premier League title hopes alive.
Petr Cech will be unavailable to Mourinho after sustaining a dislocated shoulder in last week's UEFA Champions League semi-final first leg at Atletico Madrid.
Schwarzer came off the bench to see out a 0-0 draw at the Vicente Calderon but, with the second leg to fcome on Wednesday, Mourinho is concerned the Australian could pick up an injury of his own, especially in one-on-one challenges with Liverpool strikers.
That opens the door for Hilario to make his first Chelsea appearance since August 2011 - when he kept goal in a 3-1 win over Norwich City at Stamford Bridge - and Mourinho has full faith in the 38-year-old to step up.
"It's a big dilemma," Mourinho told the club's official website.
"Especially with players who are always looking for penalties and go for contact with the goalkeeper, it's even more dangerous.
"I remember when Hilario played against Barcelona in the Champions League (in October 2006), he went in goal and he had to answer, so it's a good thing to have a second or third keeper with experience, who goes into the game ready."
