The Reds' best openings fell to Divock Origi, but he miscued a volley in the first half and was later denied by a fine last-ditch tackle.
He almost rounded the keeper late on, forcing a save in one of few chances.
Simon Mignolet made one routine save to deny Ebenezer Assifuah as Liverpool maintained their unbeaten record in this season's competition.
Sion were playing in the group stage of their first major European competition and managed to progress
A goalless draw with a side sixth in the Swiss Super League will hardly list among Liverpool's finer European nights, but the sight of club captain Jordan Henderson making his first start since August is an undoubted positive for manager Jurgen Klopp.
Philippe Coutinho appeared after 60 minutes after four games out with a hamstring complaint but not even his creativity could forge a meaningful opening as both sides struggled on a pitch which was partially frozen.
Origi - whose significance to Liverpool increased with news of another injury setback to Daniel Sturridge on Tuesday - was willing throughout but should have been more clinical.
As the 20-year-old broke through the home defence in the second period, his attempt to round Andris Vanins in the home goal lacked intent, and despite stretching he could not connect with an inviting cross late on.
The peripheral nature of summer signing Roberto Firmino was out of character given his recent impressive form, but Liverpool - who qualify with Sion - will welcome another solid display under Klopp, who now has tasted defeat just twice in 13 matches in charge.
"I am really satisfied, no-one is injured and they were very focused and concentrated on the game," said Klopp afterwards.