Venter - who will leave Warriors to join Brive next season - is one of several key players who will be available to Franco Smith for the visit of the South Africans.
Speaking to The Offside Line, Smith said: "There's a number of players due back for the Stormers game.
"Rory Sutherland is close after a shoulder injury, Sam Talakai is back from Australia, Max Williamson is ready again after a minor issue, and Henco Venter returns from suspension.
"Jack Mann has recovered, Sione Vailanu was just rested this week, and most of our backs are available - aside from Duncan Weir, who's out for the season."
Matt and Zander Fagerson, as well as Gregor Brown, remain injury doubts for the quarter-final. Jack Dempsey and Josh McKay are both making good progress and could still come into contention.
The Stormers will be without Springbok star Damian Willemse was shown a red card for a dangerous tackle during last weekend's clash against the Dragons.
Glasgow chalked up a good away win over Stormers earlier this season, and will be backing themselves to come away with a win at Sccotstoun.
"The Stormers are a team we love playing against," said Warriors captain Kyle Steyn. "We've got a lot of respect for them because they're fighters as well. Under Dobbo, they come out firing for 80 minutes. That won't change, and they'll probably be even more desperate to get one over us."