Mancini was said to have reached agreement to become the next Italy coach last Tuesday, Gazzetta dello Sport reported, but he denied that on Sunday.
Earlier in the day the club confirmed Mancini would be leaving the Russian Premier League club.
"Zenit and Roberto Mancini have reached an agreement over early termination of his contract," Zenit said in a statement.
"The contract was cancelled by mutual consent of the parties without any indemnity payments."
Mancini however insisted that no arrangements concerning a possibility of his work with the Italian national side had been achieved yet.
"It would have been totally wrong to hold talks before my contract (with Zenit) had been cancelled," he told the news conference Sunday after his last match as Zenit manager.
"I cannot confirm yet that I will be Italy's next national head coach. But I will be able to hold talks about it with the Italian (football) federation pretty soon."
Mancini added that he decided to part his ways with Zenit around three months ago.
"It was my personal initiative to leave Zenit, which is related to my family circumstances," he said. "I made this decision around three months ago. And it wasn't connected to any other club or the national team.
"I don't have a feeling that I've made mistakes or my decisions (as Zenit manager) were wrong," Mancini said. "If I was able to rewind time back I would have done everything the same way."
Mancini, 53, who signed a three-year deal with Zenit last summer with an option of a two-year extension, led Zenit to a fifth-place finish in the Russian league, seven points behind the newly-crowned champions Lokomotiv Moscow.
Italian Federation (FIGC) commissioner Roberto Fabbricini said last week that Mancini, a former Man City and Inter Milan coach, had agreed in principle to become the next manager of four-time world champions Italy, who failed to qualify for the World Cup after defeat to Sweden in a two-leg playoff.
Earlier Mancini has said he would be proud to coach Italy, telling Italian radio: "If one day I got the chance to sit on the national team bench it would be something beautiful."
During his 17-year coaching career Mancini led City to their first English league title in 44 years in 2012, and won three Serie A titles with Inter Milan.
He also won Italian Cups with Inter, Fiorentina and Lazio.
Italy have been without a permanent coach since Gian Piero Ventura was sacked after they failed to qualify for the World Cup for the first time in 60 years after losing to Sweden in November.