Begovic, who has just returned from the FIFA World Cup following Bosnia-Herzegovina's group-stage exit, has proven himself as one of the best keepers in the Premier League since joining Stoke in 2010.
His impressive performances for the Britannia Stadium outfit have attracted attention from a host of clubs, with speculation mounting that Real coach Carlo Ancelotti could make a move for the 27-year-old.
But Begovic claims that his focus is on the task at hand with Stoke, who kick off the domestic campaign with a home match against Aston Villa on August 16.
"As far as I'm concerned I will (start the season at Stoke)," he told TalkSport. "I've obviously just got home from Brazil. My first thoughts are to rest and recuperate and get myself ready for pre-season, which for me starts in three weeks.
"As far as I'm concerned this is where I'll be, this is where I see my future and I'm excited about training in a couple of weeks or so."
Reflecting on his time in Brazil, which yielded just one win, Begovic was keen to take the positives.
"Overall it was a fantastic experience," he said. "It was great to be part of such a tournament. The whole buzz around the country was something I'll never forget. It gives you motivation to go back to a major tournament and I hope to do that in the future.
"We were close to qualifying. It was heartbreaking not to go through because we believed in ourselves. The first game against Argentina at the Maracana was a fantastic occasion but the key game was against Nigeria (a 1-0 loss).
"They were a little bit better on the night and had a couple of decisions go their way. It was nice to finish with a win over Iran."