Warriors have taken seven points from their opening two fixtures against Sale Sharks and Toulon and a win on Friday should be enough to seal a place in the last 16.
And, after clinching the URC the hard way in South Africa last term, Glasgow assistant coach Nigel Carolan feels his side are "genuine contenders" for this season's Champions Cup.
Speaking to BBC Scotland, Carolan said: "With the way we ended last year, we've proven we're one of the best teams around when we're on it," he said.
"Of late, we're just a little bit inconsistent and there have been a lot of guys out injured but we're there or thereabouts.
"We showed in the Sale game, especially in that first half, that we can rip teams apart. It's now about delivering that week on week."
The opening 38-19 bonus-point win over Sale was followed by a single point defeat and two bonus points in Toulon, putting Warriors in a strong position in Pool 4.
From there, Carolan is targeting a run all the way to the final in Cardiff in May.
"We spoke about being genuine contenders in the URC last year and this year we're talking about being genuine contenders in the Champions Cup," said the Irishman.
"At home against Sale and away to Toulon, even with the teams that we did have out, we've shown that we're very competitive and when we put our full game together we're definitely one of the most exciting teams around."
Glasgow, beaten finalists in the second-tier Challenge Cup in 2023, currently sit second in the pool, one point behind Toulon.
After hosting Racing 92, Warriors will travel to Harlequins the following Saturday in their final group match.