The 53-year-old has been heavily linked with the Italy job, the Azzurri currently seeking a new head coach following the dismissal of Gian Piero Ventura.
Mancini signed a three-year deal with Zenit in 2017 but the Russian club confirmed on Sunday that the contract had been severed through mutual consent without any compensation payable.
"Zenit and Roberto Mancini have reached an agreement over early termination of his contract," the club said in a statement.
"The contract was cancelled by mutual consent of the parties without any indemnity payments."
Mancini's last game in charge will be Sunday's Russian Premier League home meeting with SKA-Khabarovsk.