Hassan Rouhani's request reflects Iranian efforts to possibly build on the groundbreaking exchanges with Washington that included a telephone chat last week between the new Iranian president and President Barack Obama.
Iran's immediate goal is to resume talks over its nuclear program to seek easing of Western sanctions. But Tehran also appears willing to explore expanded contacts.
The semiofficial ISNA news agency quoted Akbar Torkan, a senior government official, as saying on Monday that Rouhani wants to study the options of direct flights.
More than 1 million Iranian-Americans live in California and elsewhere.
Direct flights halted after the 1979 Islamic Revolution.