The Serie A outfit have relied on a strong partnership between Raul Albiol and Kalidou Koulibaly this season although it is likely the latter will leave at the end of the season, with Chelsea already expressing an interest.
Napoli are understood to have started planning and will turn to Kompany as a replacement as they look to strengthen their defence.
The Belgium international has been hounded by injuries over the last couple of years and has been restricted to just six appearances under Pep Guardiola this season.
Kompany remains highly regarded at the Etihad but if his injury issues don’t subside it is likely City will cut their losses and allow their skipper to move on.
The 30-year-old joined City in 2008 from Hamburg and is currently contracted to the Premier League outfit until 2019.