The Council, a conservative body of clerics and jurists, had until Tuesday to announce to the Interior Ministry which of around 700 would-be candidates it will allow to contest the June 14 poll.
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The Interior Ministry said the names of approved candidates would be announced on Wednesday, according to Iran's English-language Press TV.
Mehr said its reporter had heard a list of eight candidates approved by the Council that did not include either Rafsanjani or Mashaie. Mehr gave no source for its story and Reuters could not confirm it.
"It is worth mentioning that the Guardian Council has still not yet officially announced these names, and the listed names are just what Mehr's reporter has heard," the report said.
The eight approved candidates listed by Mehr included chief nuclear negotiator Saeed Jalili, Tehran mayor Mohammad Baqer Qalibaf, former nuclear negotiator Hassan Rohani and former foreign minister Ali Akbar Velayati.
A spokesman for the Guardian Council said on Monday that it would bar physically feeble candidates, a comment seen by many as a hint that it could disqualify the 78-year-old Rafsanjani.
Analysts regard Rafsanjani, sidelined from power over his tacit support for opposition leaders after the disputed 2009 election, as a significant challenge to Khamenei.
They say he would be likely to attract more reform-minded, liberal voters who might otherwise not vote. Rafsanjani had said he would not stand unless Khamenei approved his candidacy.
The eight candidates approved Tuesday for Iran's June 14 presidential election to replace Mahmoud Ahmadinejad, who cannot run again because of term limits are:
Ali Akbar Velayati, a Top adviser to Supreme Leader Ayatollah Ali Khamenei on international affairs. Velayati, 67, served as foreign minister during the 1980-88 war with Iraq and into the 1990s. He is a physician and runs a hospital in north Tehran. He was among the suspects named by Argentina in a 1994 bombing of a Jewish center in Buenos Aires that killed 85 people.
Mohammad Bagher Qalibaf, Tehran mayor and former commander of the Revolutionary Guard during the Iran-Iraq war. Qalibaf, 51, is a pilot who enjoys good relations with Khamenei.
Hasan Rowhani, a former nuclear negotiator and Khamenei's representative at the Supreme National Security Council, which also handles the nuclear dossier. Rowhani, 64, is a British-educated cleric.
Mohammad Reza Aref, a liberal-leaning former vice president under reformist President Mohammad Khatami. Aref, 61, a former Tehran University chancellor, vowed to drop out of race if Khatami decides to run.
Mohsen Rezaei, a former chief commander of the Revolutionary Guard. Rezaei, 58, ran in 2009, but finished fourth. He currently is secretary of the Expediency Council, which mediates between the parliament and Guardian Council.
Saeed Jalili, Iran's top nuclear negotiator since 2007. Jalili, 47, began his career as a diplomat in 1991. He has the support of ultraconservative cleric Ayatollah Mohammad Taghi Mesbah Yazdi, who was previously seen as Ahmadinejad's spiritual mentor.
Gholam Ali Haddad Adel, a 68-year-old former parliament speaker, who is currently a member of the Expediency Council and considered a strong conservative voice. His daughter is married to Khamenei's son.
Mohammad Gharazi, a former oil and telecommunications minister. Gharazi, 71, also served in parliament in the 1980s and '90s. He is considered conservative and portrays himself as a steady-handed technocrat.