United are the only English club to have completed the treble, under Sir Alex Ferguson in 1999, and while Guardiola’s City have dominated the domestic scene, they have yet to be crowned champions of Europe.
Haaland told BBC Sport: “It would be unreal to make this history. This is why they bought me of course, to get this, we don’t have to hide that.
“It would mean everything. I will do everything I possibly can to try to make it happen. It’s my biggest dream and hopefully dreams do come true.”
But the 22-year-old Norway striker warned both United and Inter will be “motivated” to “destroy” City’s treble chances.
“But as well it’s not easy,” Haaland said. “It’s two finals against two good teams that will do everything they can to try to destroy that.”
Haaland has taken the Premier League by storm in his first season, scoring a record 36 top-flight goals 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 was also named the Football Writers’ Association (FWA) men’s footballer of the year.
“I’m 196cm tall and have got long blond hair so wherever I go people are going to see me,” he said. “So that’s how my life is. What can I do?
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“There’s nothing I can do, that’s my life. I just have to try to enjoy it as much as I can. Try to relax when I’m 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 been developing in a really positive way and that’s really important for me because I’m still really young.
“I’m 22, I’ve got a long career ahead of me and I still have to develop. That’s also something I was thinking of over one year ago when I was thinking about my next move.”