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.
Reports say the Italian, 53, could be the next head coach of his country's national team.
"The contract will be terminated by mutual consent without any compensation payable". Mancini, who has reportedly been engaging in talks with Italy to take the helm of the first team, is to leave Zenit after their final league game in the 2017/2018 season against Khabarovsk.
Under-21 coach Luigi Di Biagio took the reins for March friendlies against Argentina and England.
Despite Allardyce being contracted until the end of the 2018-19 season, one fan would have Mancini "in a heartbeat", while another described him as a "tactical genius".
Mancini added that he chose to part his ways with Zenit around three months ago.
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"It has nothing to do with the club or the national team", he added.
Mancini, one of the highest-profile foreign coaches to join the Russian Premier League in recent years, signed a three-year contract with Zenit in 2017.
Mancini led City to its first English league title in 44 years in 2012, and won three Serie A titles with Inter Milan.
The four-time champions Azzurri failed to qualify for the World Cup in Russian Federation starting next month, which is their first absence in 60 years.
Mancini also revealed that that he now had no agreement with the Italian team and could not confirm he would be named to the post.