The Azzurri are seeking a new boss after parting company with Gian Piero Ventura earlier this week, less than 48 hours on from their 1-0 aggregate defeat to Sweden that cost them a place at the 2018 World Cup.
Speaking to Russian TV channel Match TV, however, Mancini distanced himself from the job as he wants to remain in charge of Zenit.
"I am not surprised my name has been mentioned on the list, seeing as they also discussed colleagues with experience who won in various different countries," he said.
"But I am happy at Zenit and in St Petersburg, so I am not thinking about the Nazionale. My objective is to win the Russian league title."
Mancini won the Premier League and FA Cup during his three-and-a-half years at Man City, before being sacked and taking on roles at Galatasaray, Inter Milan and Zenit.