Tony Pulis' side have travelled to Switzerland to take on the Super League leaders in impressive form, having beaten Hajduk Split over two legs and held Chelsea to a goalless draw in their Premier League opener.
Bosnia-Herzegovina international Begovic kept clean sheets in all three of those games, but on Thursday night will face a side who thrashed Lausanne Sport 5-2 at the weekend.
"From a defensive point of view, we have been superb so far, so we will go there confident of producing another solid performance," Begovic told Stoke's official website.
"It will be tough - we know that. There are no easy rides anywhere when you are playing home or away in European competition.
"They are flying at the moment, but we are confident too. We beat a very good Hajduk Split side 2-0 in the last round and held Chelsea to a draw on Sunday, so we are going there looking to put ourselves in the driving seat."
The former Portsmouth goalkeeper has established himself as the Potters number one ahead of Thomas Sorensen, but knows he cannot afford to let his standards drop.
"It's fantastic to be involved in these competitions - it's what you aim for as a youngster, so of course you want to play in as many games as possible," he said.
"There is competition for places now and nothing is guaranteed, but I'm obviously hoping to keep my place in the team and help the club to another successful season."
Former West Ham centre-back Matthew Upson is in line to make his Stoke debut against Thun.
Upson joined the Potters last week and, with fellow new signing Jonathan Woodgate to be rested, the England international is set to play.
Rory Delap (hamstring) and Jermaine Pennant (thigh) may not be risked but winger Matthew Etherington is in contention.
The 30-year-old was a doubt due to an arm injury sustained against Chelsea but scans have shown he has only suffered minor nerve damage.
The 30-year-old flew to Switzerland with the rest of the squad and Pulis must now decide whether he is ready to start.
"Once we've trained on the artificial pitch and got a feel for it, I will talk to the medical team about one or two players who have knocks and Matty is one of them," said Pulis.
"It's obviously a huge relief that the injury to Matty is not serious, but he is still a bit sore. Like some of our other more experienced players, he knows his body better than anyone. So I will speak with him and the medical team before I make a decision."