This was reported on Friday by The Washington Post with the reference to official representatives in the US Administration and the Iranian government. The name of the Bush family member has not been yet announced.
The proper request was sent by Washington to Tehran on Tuesday, December 30th and now the US side waits for a response from Iran.
In case the response is positive, the current US delegation will be the first delegation of this level visiting Iran since 1979, when the Islamic revolution overthrew the pro-American regime of Nadir Shah Pahlavi and resulted in the complete breakup of the American-Iranian relations.
However, representatives in the Bush administration stress that the mission of the delegation is purely humanitarian.
Immediately after the earthquake the US sent to Iran a delegation consisting of 84 rescuers.