The proposals come in a letter from Hassan Rowhani, a moderate in Iran's Shia cleric-led ruling establishment, to Time magazine, posted on its website on Wednesday.
It comes days after a letter sent by Mahmoud Ahmadinejad, Iran's president, to the US president that Tehran said was aimed at resolving the two countries' differences.
But the 18-page message did not address the nuclear issue and Washington dismissed it.
Rowhani - Iran's former top nuclear negotiator until he was removed by Ahmadinejad last year - laid out an eight-point scenario for resolving the standoff.
More UN inspections
He suggested doing this by strengthening UN inspections of Iranian nuclear facilities to ensure it cannot develop nuclear weapons but without giving up uranium enrichment as the United Nations has demanded.
In the letter, he underlined that the proposals were his personal opinion, rather than an official Iranian position.
But Rowhani is close to Ayatollah Ali Khamenei, Iran's supreme leader who holds final say in all matters in Iran.
He is Khamenei's representative on the Supreme National Security Council, which oversees Iran's nuclear negotiations with the outside world.
Rowhani is also a member of the Assembly of Experts, a council that chooses or dismisses the supreme leader.
Ahmadinejad has sought to sideline Rowhani, sharply criticising compromises made while he was top negotiator.
In the letter, Rowhani said Iran would "consider ratifying" the Additional Protocol to the Nuclear Non-proliferation Treaty (NPT), which allows the UN's International Atomic Energy Agency (IAEA) to conduct surprise inspections of its nuclear facilities and inspect other facilities not officially declared as nuclear sites.
Iran signed the Additional Protocol in 2003 but it was never ratified by parliament. Nevertheless, Tehran allowed IAEA inspectors to carry out surprise inspections including 26 visits to military facilities under the protocol until February, when Iran ended all voluntary co-operation with the agency amid the escalating confrontation with the West.
Rowhani said Iran would also "address the question of preventing break-out from the NPT", the international pact under which nations commit not to produce nuclear weapons.
He said the UN Security Council should set a "fixed period" for Iran and the IAEA the negotiate a "credible plan" with his ideas.