Inter and Roma denied another final date
The two sides have clashed in five of the last six Italian Cup finals with Inter prevailing last season on their way to a treble.
Juventus are also in the first half of the draw but AC Milan are in the second part, meaning a final showdown with Inter is possible.
The first round, involving lower-division clubs, takes place on August 8 and will be followed by three more rounds before the big Serie A teams enter at the last-16 stage in December or January.
The Serie A fixture list for the new season, starting on August 28, will be announced on Wednesday.