“Based on an idea put forth during [Mr Amirabdollahian's] meeting with Saudi Crown Prince Mohammad bin Salman, Iran is ready to sign a comprehensive partnership agreement with the kingdom,” the Iranian Foreign Ministry said on Saturday.
Mr Amirabdollahian met his Saudi counterpart, Faisal bin Farhan, on the sidelines of the UN General Assembly in New York on Saturday.
Saudi Arabia confirmed the meeting and said the two sides had reviewed "joint relations and ways to strengthen and develop them in all fields", state outlet Spa reported.
Riyadh did not provide any comment on the prospect of a deal with Tehran or provide further details.
During the meeting, Mr Amirabdollahian and Prince Faisal “referred to the firm resolve” of the two countries to enter a new phase in their relations, and expressed pleasure with the reopening of their embassies in Tehran and Riyadh and the exchange of ambassadors by the two countries, Tehran said.
Mr Amirabdollahian said it was necessary for Tehran and Riyadh to launch a “joint economic commission to expand their ties in different areas, especially in the trade and economic” fields.
He stressed the need to reinstate and open air and shipping routes to facilitate travelling and trade between the two countries.
According to the Iranian Foreign Ministry, Riyadh is willing to strengthen co-operation and put into action their proposed ideas, adding that a meeting between the countries' heads of state will accelerate the pace of co-operation.
Saudi Arabia's Permanent Representative to the UN Abdulaziz Al Wasil and director general of the Foreign Minister's Office Abdulrahman Al Dawood also attended the meeting, the ministry said.
Earlier this month, Saudi Arabia’s ambassador to Iran, Abdullah Al Anazi, arrived in Tehran as his Iranian counterpart Alireza Enayati landed in Riyadh to start his duties as envoy to the kingdom.
Last month, Saudi Arabia's Crown Prince Mohammed bin Salman met Mr Amirabdollahian, while King Salman extended an invitation to Iranian President Ibrahim Raisi to visit the kingdom.
The countries reopened their embassies and consulates and reinstated economic agreements signed more than 20 years ago.
Saudi Arabia and Iran agreed to re-establish diplomatic relations following China-mediated talks in April.