The Warriors lifted the URC trophy in 2024 for the first time in nine years and currently sit second in the league standings, while also completing a perfect group-stage campaign in Europe.
Their Champions Cup journey continues in April with a home round-of-16 tie against the Bulls at Scotstoun, and the 20-year-old is confident the squad can rise to the challenge.
When asked if winning both competitions was a stretch, Stephen told BBC Scotland: "I don't think so.
"That's definitely something Franco has mentioned to us. It would be pretty special to do that.
"I don't know if it's been done before but I definitely think we've got the capabilities to do it."
Stephen has featured as a replacement in all four of Glasgow's Champions Cup wins this season, and has enjoyed and learned from the challenges he's faced.
"You've got to kind of adapt to what the level is and especially playing different styles of rugby. The French play with a lot of flair and are very attacking. So trying to adapt to how they play their game, learn different ways of defending or attacking - I've found that pretty helpful for my game."
The last side to achieve the Champions Cup and URC double was Leinster in the 2017-18 season - a milestone Stephen and his teammates are now aiming to emulate.