The Arab News daily reported that three of the suspects are alleged "terrorists" while another is accused of espionage.
It gave no details of the accusations.
Saudi-Iran row: Pakistan, Turkey urged to help end crisis
The Saudi Gazette said they were arrested in 2013 and 2014, but did not identify them.
A fifth Iranian is already serving a 13-year jail term following his conviction for recruiting young Saudis to fight in neighbouring countries, the newspapers said.
The reports come after tensions escalated between Riyadh and Tehran.
Diplomatic spat: Saudi-Iran crisis widens as Kuwait recalls envoy
Saudi Arabia severed diplomatic ties and air links with Tehran after crowds set fire to its embassy in the Iranian capital and its consulate in second city Mashhad last weekend.
The protests were in response to Riyadh's execution of Shia cleric Nimr al Nimr, a driving force behind demonstrations in 2011 by the kingdom's Shia minority.
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