Mancini is currently in charge of Zenit St Petersburg.
"We have to start talks soon," former Milan defender Costacurta admitted.
“There's no hurry but we need to make moves as soon as possible so we can talk to the,. The names are the ones you've already heard, people who have shared a lot of matches with me, and also military service.
“Like Mancini, just to use one of the palatable names. [Antonio] Conte did a sporting miracle at the last Euros."