Stoke finished in eighth place last season and Begovic has revealed that they are aiming to build on that position this campaign, as they look to move forward under Mark Hughes' stewardship.
"We've got a good squad, a great manager and I think we can achieve a lot of good things," he is quoted as saying by FourFourTwo. "If we can establish ourselves in the top 10 then that would be fantastic, and a really big achievement."
The Potters have made an inconsistent start to the season, where their usual strong home form has not been evident.
Stoke have built their success in recent times on making the Britannia Stadium a fortress, but this season they have looked better on the road.
Hughes' men have lost to Aston Villa and Leicester City in front of their own supporters, but are unbeaten away so far.
The side have collected four points from their opening two games on their travels - with a draw against Hull City and a win against Manchester City.
The victory over City was a signal of Stoke's increased attacking threat that Hughes has brought and it will be a triumph which breeds confidence for the squad.
Indeed, although their first game back after the international break ended in disappointing circumstances, with a 1-0 defeat to Leicester, Begovic has urged fans not to be concerned.
He said: "The Premier League now undoubtedly is the most competitive league in the whole world and anyone can beat anyone on any given day."
"Leicester defended really well, had a good game plan, caught us on the counter-attack and made the most of their one chance."
"It was one of those difficult days that happen in football but we move forward and if we keep putting the right effort into the game we'll get the right results."