Former Inter Milan boss Mancini is among the favourites for the post.
"When you're abroad you always miss your country," Mancini said.
“You see the national team playing and it takes you back to the past, the 70s and the 80s, with great emotion.
“You never know in life, I think that coaching Italy one day would be an extraordinary thing.
“In the meantime though I'll try to win and do my best with Zenit."