The 58-year-old is wanted by his national side after being sacked from Bayern Munich last month, according to The Sun.
The Azzurri failed to automatically qualify for the World Cup from Group G and now have to contest the playoffs next month.
Plans have allegedly been drawn up to replace current coach Gian Piero Ventura after Russia 2018 or sooner, should the side lose in the playoffs.
However, Ancelotti reportedly told the Italian FA that he would like to take the rest of the season as a sabbatical before making a return to club management.
The former Chelsea manager has been linked with both Arsenal and Liverpool, as well as the Blues if he is asked to replace Antonio Conte in the summer.