The Blues are through to a Champions League semi-final meeting with Barcelona, tackle Arsenal in the last four of the FA Cup on Saturday and remain in the Premier League title chase.
Ballack and his team-mates narrowly missed out on three trophies last term as they were undone by Tottenham in the Carling Cup final before Manchester United proved to be their nemesis in both the Premier League and Champions League.
And the Germany international believes they can challenge on all three fronts under Guus Hiddink after their barren campaign when Avram Grant replaced Jose Mourinho.
Ballack told the Evening Standard: "The team are hungry after finishing runners-up three times last season.
"We are not a team who have won everything in the past. If you compare us to Liverpool, they have had big success.
"But now we are smelling the success. We are coming close to winning something. This club need a big title to go further and that's what we are trying for.
"I want to win something. I have a few years ahead but I will give everything for the rest of the season to win one, two or three trophies."
Ballack is out for revenge against the Gunners after Arsene Wenger's men came from behind to triumph 2-1 at Stamford Bridge in the Premier League earlier in the season.
He said: "We want to show Arsenal we can beat them after what happened before. We were controlling the game until they scored an offside goal.
"Getting to the Champions League semi-final has given us a confidence boost going into another big game. Arsenal have a squad and a team that can play football but sometimes they can be up and down.
"That is why they are sometimes not at the top of the League but, if they play at their highest level, they can play fantastic football."