The official, who requested anonymity because he was not authorised to speak to the media, said the dates of the visits were yet to be finalised.
The premier is now on an official visit of China after he had arrived in Beijing on October 8.
The visit to Iran may prove to be very crucial as reports last month suggested that the premier had offered to act as mediator in order to defuse the increasing tensions in the Middle East. Both Saudi Arabia and the United States blamed Iran for the drone strikes - a charge Tehran has strongly rebutted.
Iran also welcomes the offer from Yemen's Houthi movement for a truce, the president's chief of staff underlined, saying it would be a "positive stop" for Saudi Arabia to be looking to mend ties with Iran and settle the crisis in Yemen.
"In a situation where the Saudis would like to negotiate with Iran, if they pursue regional issues at the negotiating table and not by killing people, they will certainly have the Islamic Republic along with them", Foreign Minister Mohammad Javad Zarif said, according to the official IRIB news agency.
Prime Minister Imran Khan held meetings with Donald Trump and Iranian President Hassan Rouhani on the sidelines of the United Nations General Assembly session. Before departing to NY. He has also traveled to Saudi Arabia five times.
Pakistan has been pushing for mediation in the Middle East since it fears that any conflict between the two key Muslim countries would have serious implications for the country.
However, it emerged earlier that PM Khan will visit Saudi Arabia on October 29 to participate in three-day Future Investment Initiative (FII) 2019 in Riyadh over the invitation of Saudi King Salman bin Abdulaziz Al Saud.
Saudi Arabia will host its first-ever worldwide tennis tournament later this year, offering a prize fund of US$3 million.