It is a diplomatic flirtation between the two most powerful nations in the Middle East, but neither appears ready to take the plunge into a full relationship.
A resumption of formal ties between Iran and Egypt after a 31-year-old rupture could have serious repercussions in the region.
Tehran's state-run Press TV reported on Monday that Iran had appointed an ambassador to Cairo, Ali Akbar Sibuyeh, a career diplomat who is the son of a prominent cleric.
Iran's foreign ministry yesterday declined to confirm the report, saying it was "hasty" and "guesswork". But it maintained that developing relations with Egypt was in the interests of both nations and of the region.
Egypt's foreign ministry also denied reports that an Iranian ambassador to Cairo had been appointed.
Earlier this month, however, Egypt's new foreign minister, Nabil Elaraby, said Cairo did not consider Tehran an enemy and would open "a new page with all countries, including Iran."
Key to an historic breakthrough will be the resolution of a long dispute over a street name and a 10-metre-high mural in Tehran's business district. Both celebrate Khaled Islambouli, the ringleader of the assassins who killed Egyptian president Anwar Sadat in 1981, three years after Sadat signed the Arab world's first peace treaty with Israel.
"It is not clear if this issue has been resolved, or whether Egypt's new government will put up with the offensive street name not being changed," a European former ambassador to Iran said.
Tehran severed ties with Egypt a year after Iran's 1979 Islamic Revolution in protest at Cairo's recognition of Israel.
A rapprochement between the countries is likely to concern pro-Western Arab countries, unnerve Israel and dismay the United States.
Egypt under Hosni Mubarak mistrusted Iran and enjoyed strong relations with the US and Saudi Arabia as a Sunni bulwark against the Shiite Islamic republic.
The European former ambassador said it is little known that Mr Mubarak's regime maintained high-level diplomacy with Iran that stopped just short of normal relations.
"The US will have to swallow much more" because the Egyptian public will expect Cairo to alter its relationship with Israel, he said in a telephone interview.
Egyptian foreign ministry officials said on Monday that Mr Elaraby is considering a visit to the Gaza Strip, which is controlled by Hamas. Iran supports Hamas but Mr Mubarak's administration shunned it.
Mr Elaraby also stoked Israeli concerns earlier this month by describing Hizbollah as part of Lebanon's political and social fabric and saying that Egypt welcomed contacts with the Iranian-backed organisation.
Cairo's outreach under its transitional government has also extended to Syria, a key Iranian ally and a historic enemy of Israel.
By recalibrating its foreign policy, while maintaining a good but more balanced relationship with the US, Cairo aims to regain its position as the region's main power broker.
Central to the new Egypt's foreign policy ambitions will be a resolution of the Palestinian issue, which would be immensely popular with the Egyptian public.
