The Serie A giants have been linked with a move for the Bosnia international, who will be seen as a direct replacement for Edinson Cavani.
The Uruguayan looks likely to leave Napoli this summer and coach Rafael Benitez is reported to have Dzeko at the top of his list.
Mancini has now backed the move, insisting that the 27-year-old will guarantee 25 goals a season.
"If Napoli take Dzeko, they would be safe," Mancini told reporters. "They would get a great striker who gets 25 [goals] a season and only has one defect - that he wants to play in every game."
Dzeko joined City from Wolfsburg for £27m in 2011.