Prime Minister Imran Khan, who was accompanied by Foreign Minister Shah Mehmood Qureshi and head of the Inter-Services Intelligence (ISI), put forward the proposal during his visit to Tehran on Sunday, the officials told the newspaper on Monday.
According to the officials, Khan told Iranian leadership that Pakistan was not only ready to facilitate the dialogue but also willing to arrange face-to-face talks in Islamabad.
The Iranian side expressed their inclination towards the proposal with "some caveats", they added.
The Prime Minister will now take the same proposal to Riyadh when he is scheduled to arrive on Tuesday and meet Crown Prince Mohammed bin Salman to discuss peace efforts.
One of the officials told The Express Tribune that Pakistan's proposal was aimed at opening some channels of communication between the Saudi and Iranian authorities at a time when tensions between the two arch rivals have been building up following the September 14 drone attacks on a processing plant and an oil facility in the Kingdom.
Riyadh and Washington blamed Tehran for being behind the drone attacks, a charge Tehran strongly rebutted.
Yemen's Houthi rebels on the other hand claimed the attacks. The unprecedented attacks have raised the specter of a potential conflict between Iran and Saudi Arabia.
When asked to comment on the success of Pakistan's diplomatic initiative, the official acknowledged that the issues between the two countries were complicated and required sustained efforts.
The mediation initiative is being taken at the request of Saudi Arabia. The Crown Prince had during Khan's last visit to Saudi Arabia asked him to help defuse tensions with Iran as Riyadh wanted to avoid war.
( With inputs from IANS )