Zinedine Zidane's team will take on Bundesliga giants Borussia Dortmund, Sporting CP and Legia Warsaw in Group F following Thursday's draw in Monaco.
This season's final takes place in the Welsh capital, where Madrid collected the UEFA Super Cup in 2014, following Champions League glory in Bale's first season at the club.
Now, with two European titles under his belt and a run to the Euro 2016 semi-finals with Wales fresh in the memory, the 27-year-old forward is setting his sights high for the coming campaign.
"It’s obviously a difficult group, it always is in the Champions League. All the teams are very good," he told BT Sport.
"We fancy our chances to get through. We know there are going to be some difficult games and we'll prepare like we always do.
"I'm building my fitness up slowly. I've only been back for two-and-a-half weeks now. I have to get up to speed as quick as I can. I'm looking forward to the season ahead and hopefully some more trophies in Cardiff.
"It would be very nice. I've experienced the Super Cup in Cardiff before and it would be amazing to experience an actual Champions League final in Cardiff as well."
Bale fell short in his quest for individual honours as his Madrid team-mate Cristiano Ronaldo was named Best Player in Europe in a presentation immediately after the Champions League draw.
Having been in the running alongside Atletico Madrid and France forward Antoine Griezmann, Bale said: "Obviously congratulations to Cristiano, it's well deserved. It was a great experience to be here.
"I would have liked to have won the award, like anyone would. I suppose it’s a sign that I'm improving and doing well on the pitch."
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