Okaz newspaper, quoting informed sources, said on Sunday the network's security chief Saif al-Adil gave orders for the attack in the capital Riyadh by satellite phone.
Neither Saudi nor Iranian officials were immediately available to comment on the report.
"The sources said Saif al-Adil led the bombing operation of the Muhaya residential compound, using a Thuraya phone to give instructions to the terrorists in the kingdom who carried out the criminal operation," the Arabic-language daily said.
"The sources said that the terrorist Saif al-Adil is in Iran," it added.
At least 18 people were killed in the Muhaya bombing two weeks ago, blamed on Saudi-born Usama bin Ladin's al-Qaida network. The attack followed triple bombings in Riyadh in May which killed 35 people.
The newspaper said Saif al-Adil fled to Iran with 500 al-Qaida members during the intensive US bombing of Afghanistan in late 2001. It said they were detained by Iranian troops.
Some al-Qaida members in northern Iran were in touch with figures outside,including Bin Ladin, it added.
Asked on Sunday about US media reports that Bin Ladin and top al-Qaida figures may be in Iran, an Iranian Foreign Ministry spokesman told reporters in Tehran: "These are rumours... We are serious about confronting al-Qaida. We have always been and will continue to be so."
Iran has said it arrested a number of al-Qaida members, including some senior figures, but has declined to name them and says it will not hand them over to US officials for questioning.
Last month, Tehran said it had given the names of extradited al-Qaida suspects to the UN Security Council but declined to give any details of detainees remaining in the country.
Western intelligence sources and media reports suggest Iran may be holding Saif al-Adil.
Washington has in the past accused Iran of sheltering al-Qaida and said members of the network in Iran may have planned the May bombings in Riyadh. Iran denied the charges.