The Premier League champions play Manchester United in the FA Cup final before facing Inter Milan in the Champions League final.
Pep Guardiola’s side won their fifth Premier League title in six seasons and play Manchester United in Saturday’s FA Cup final before facing Inter Milan in the Champions League final on June 10.
United are the only English club to complete the treble under Sir Alex Ferguson in 1999, and while Guardiola’s City have dominated the domestic scene, they have yet to be crowned European champions.
Haaland told BBC Sport: “It would be incredible to make history. That’s why of course they bought me to get it, we don’t have to hide it.
“It would mean everything. I will do my best to try to make it happen. It’s my biggest dream and I hope dreams come true.”
But the 22-year-old Norwegian striker warned that both United and Inter will be “motivated” to “destroy” City’s treble chances.
“But it’s not easy either,” Haaland said. “It’s two finals against two good teams who will do everything they can to try and destroy it.
Haaland took the Premier League by storm in his first season, scoring a record 36 goals in the top flight and 52 in all competitions.
He is the first player to be voted Premier League Player and Young Player of the Year in the same season and has also been named the Football Writers’ Association (FWA) Men’s Footballer of the Year.
The former Salzburg and Borussia Dortmund striker said success in England changed his life.
“I’m 196cm tall and I have long blonde hair, so wherever I go people see me,” he said. “So this is my life. What can I do?
“I can’t do anything, it’s my life. I just have to try to enjoy it as much as possible. Try to relax when I’m at home with good people around me, that’s really important. Just try to enjoy my life.”
Haaland said he was still not the finished article, adding: “I’ve developed in a really positive way and that’s really important for me because I’m still really young.
“I’m 22, I have a long career ahead of me and I still have to develop. That’s also something I thought about over a year ago when I was thinking about my next move.”