Torres, who is hoping to start Chelsea's Champions League semi-final first leg against Barcelona on Wednesday, has tasted both World Cup and European Championship glory with Spain in the last four years.
But the striker has yet to win a major trophy at club level, and he told the club's official website: "I never really thought about winning the World Cup as I thought it was impossible, but now I have achieved that and I know what it feels like, so to win the Champions League would be a dream come true."
No club has gone closer to winning the Champions League in the last decade without doing so than Chelsea, who thought buying Torres would finally lead them to that aim.
Torres told the club's official website: "I know the ambitions this club have in terms of winning the Champions League, but it's the same as what I have myself. It's something I dreamt about as a youngster growing up.
"It was the only trophy I wanted as a kid, to hold it in my arms, and if we do manage to win it, I'm sure it will be one of the greatest moments of my life."
Torres, who ended last season empty handed after his move from Liverpool looked to have backfired, also has an FA Cup final against his former club to look forward to.
He added: "There isn't one single club in the world that can guarantee trophies, but top teams like Chelsea are always fighting for them, so now it's time to be patient, build a great team and it's good for me to be involved with such a good side, like the one we have now.
"There's still one month left in the season, we're in the final of the FA Cup, the semi-finals of the Champions League, and this is what I want.
"Whether you win or not, that is down to football, but we are there and that's the main thing."
Source: PA
Source: PA