City have already signed defender Jerome Boateng from Hamburg but look set to reinforce further up the field, with an array of big names linked.
CSKA Moscow winger Krasic had looked certain to move to Italy, with Juventus and Inter Milan strongly interested, while Wolfsburg striker Dzeko has frequently been linked with the biggest clubs in Europe, but Mancini appears hopeful of adding one of the duo to his squad.
"Many players are linked with City, often for convenience," he told Tuttosport. "We are used to raised prices, but in reality we cannot buy dozens of players. Of course we aim to strengthen. Krasic or Dzeko? One really interests us, the other doesn't. Who? I cannot say."
Ibrahimovic, who played under Mancini at Inter, is also said to be a target for City, with rumours in recent weeks over a swap move with Robinho. "In my opinion, Ibra is the best striker in Europe," Mancini said. "It makes me laugh when people say he misses crucial chances."