Dzeko’s Roma future is in doubt after the former Manchester City striker, 34, fell out with manager Paulo Fonseca.
It is understood Roma initiated the contact with Inter, who signed Sanchez from Manchester United on a three-year deal in August after a year on loan.
The 32-year-old has scored just twice this season, and boss Antonio Conte is open to the move.
Both clubs are still in contention for the Serie A title in Italy. Inter are second, two points behind leaders AC Milan, and Roma third as the campaign reaches its halfway stage.