The Premier League club has lodged a request with European football's governing body and Gerrard said Liverpool should not have to play on the day when the 96 people who died will be remembered.
"We hope that UEFA show some common sense," Gerrard, who grew up in Liverpool and lost a cousin in the disaster, told the club's website on Sunday.
"You would think they would accept the significance of the date for the people of Liverpool but unfortunately feelings like that don't always come into it."
UEFA have yet to confirm whether Liverpool will have to play on the day. The draw for the last eight is on Friday.
"We're still waiting to see whether UEFA will make us play on the day. That would be far from ideal given all the emotion that always surrounds the club on that day," said Gerrard.
"It should be a time that Liverpool Football Club remembers the people who were lost and their families.
"Hillsborough is always on my mind because I lost a member of my family there and any success we get as a club this year will be dedicated to those people who lost their lives."
The disaster happened shortly before Liverpool's FA Cup semi-final against Nottingham Forest when Liverpool fans packed in behind a goal at Sheffield Wednesday's Hillsborough ground were crushed to death.
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