Torres was presented to the media as a Chelsea player on Friday following his British record £50 million to Stamford Bridge, but Mancini has revealed City were in contention for his signature prior to the start of the season.
"Maybe in the summer we tried but it was difficult," Mancini said. "He is a fantastic player. Maybe it was time to change shirts because he wanted to leave.
"He is one of the best strikers in Europe and I am sure he will be fantastic for Chelsea. For us, we have bought Dzeko and are happy with him. He is like Torres."
Mancini's current focus is Saturday's Premier League tie against West Brom, as he seeks to arrest a downturn in form that has seen City slip eight points behind Manchester United, having played a game more than the league leaders.
The Italian's side have been uncharacteristically sloppy in defence of late and Mancini readily admits he would sacrifice excitement for solidity.
"I would like this," said Mancini, when asked if his team needed to become more boring. "When you don't concede a goal but you have players like Carlos, Dzeko, (David) Silva and Yaya Toure, you win 90% of your matches.
"At this moment, I would prefer it if we win 1-0 for two or three games. We would like to score two or three goals every game but it is not possible and in the past, all the teams that have won the title conceded very few goals."
There have been suggestions that Mancini is prepared to drop goalkeeper Joe Hart, who on Friday morning denied suggestions that he is suffering from a lack of focus. However, the City manager appeared to place his faith in his current No. 1 when saying: "Joe is the best goalkeeper in England."