No details were given on the nature of the trips, or when they might begin.
Possible attractions would include the plants at Isfahan and Natanz, or a reactor being built in Bushehr.
The reported proposal comes after the UN Security Council has told Tehran to halt uranium enrichment, amid fears it is trying to build nuclear arms.
Iran maintains it has a right to a nuclear programme, which it says is purely for civilian purposes.
‘Peaceful’
So far United Nations atomic watchdog inspectors and reporters are the only foreigners believed to have been allowed to visit the controversial sites.
The head of Iran’s tourism organisation said President Mahmoud Ahmadinejad had asked his group to study ways for tourists to see the sites, state news agency Irna reported.
“This authorisation has been issued since the Iranian nuclear activities are peaceful,” Esfandyar Rahim Mashaii told the agency.
