Barcelona won the Copa del Rey with a stunning 4-1 win over Athletic Bilbao at the Mestalla, and were crowned La Liga champions at the weekend when Real Madrid lost to Villarreal.
Next up is the Champions League final against Manchester United on May 27, and Messi has set his sights on the treble.
He told the Clarin newspaper: “I don’t mean what we have achieved so far is not a big achievement.
“I say this team is focused on clinching the goal we had set in the beginning of the season, when more than one person thought we were too ambitious.
“You can search in the archive and you’ll see that, since (coach Pep) Guardiola’s arrival, we have said we want the Copa (del Rey), La Liga and the Champions League.
“Guardiola is a great coach who changed important details. In the match against Real Madrid, he played me as a main forward but a little bit behind. I was truly surprised. I thought I was not going to touch the ball, but I played in great form and we claimed a historic 6-2 win.”
Messi will go head to head with compatriot Carlos Tevez in Rome on Wednesday week, and is full of respect for his international team-mate.
“He won the league with Manchester United. He is great. He has won about a thousand titles,” said Messi.
The final will also see 2008 FIFA World Player of the Year Cristiano Ronaldo do battle with Messi – the player he pipped to that title.
“Cristiano Ronaldo is a great player. His long-distance shots are terrific,” he said.
“I am not his friend because I don’t see him too much, but I am sure he has the same thought I have. None of us play to be the best of the world. This is a team game.
“I want the treble and I don’t deny it. I’d love it because it was the goal we set in the beginning of the season, when it was almost impossible. Being the best on earth is another thing.”
When he has conquered Europe with his club, Messi wants World Cup success with Argentina.
“I want the triple crown and then the 2010 World Cup with Argentina, obviously,” he said.
“I still remember the celebration when we won the Under-20 World Cup in Holland in 2005. Repeating that in the senior squad, under (Argentina coach Diego) Maradona, would be completely unique and unforgettable.
“Now we are going towards the triple crown. Everything is going so well that we will really enjoy it if we achieve that.”