Former Milan boss Montella succeeded Eduardo Berizzo at the Ramon Sanchez Pizjuan at the end of December and led the LaLiga side to a shock Champions League triumph over Manchester United this month.
Italy are yet to identify a permanent replacement for Gian Piero Ventura, who failed to secure qualification for the 2018 World Cup.
However, speaking ahead of Sevilla's home game against Barcelona, the 43-year-old insisted he does not see himself in the Azzurri dugout for some time yet.
"There is no chance to become manager of the Italian team," he told a news conference.
"Firstly I feel very good here and I am focused on what I am doing here. Secondly there wasn't any kind of contact from Italy.
"The third reason is that to coach Italy you must have many white hairs and for now I have just a few."
Italian Football Federation (FICG) vice-commissioner Alessandro Costacurta has identified Chelsea boss Antonio Conte as his main target, with Di Biagio and Zenit's former Manchester City manager Roberto Mancini also in the frame.
Italy lost 2-0 to Argentina in Manchester last Friday before Lorenzo Insigne's late penalty salvaged a 1-1 draw against England at Wembley.