The Dutch were World Cup finalists in South Africa two years ago and Sneijder believes that under the stewardship of coach Bert van Marwijk they are well equipped to go all the way in Poland and Ukraine.
"The changes Bert van Marwijk has made to our style of play since taking over have proven to be quite successful as we reached the final at the World Cup," Sneijder told De Telegraaf.
"We are now aiming to reach at least the final at Euro 2012. We want to do even better, though, and win the European title."
Holland's preparations for the tournament suffered a setback in Amsterdam at the weekend when they were beaten 2-1 by Bulgaria in a friendly.
The Oranje were at near full-strength, with Robin van Persie partnering Klass Jan Huntelaar up front, but came in for heavy criticism from former boss Marco van Basten.
Van Basten claimed his successor Van Marwijk had been too defensive, which has drawn the ire of Sneijder.
"His attitude toward Van Marwijk and the team was a bit strange. It was not the right thing to do, and showed a lack of collegiality," Sneijder said.
"Of course he has the right to voice his opinion, but I'd have expected better of him."