Iran's top diplomat made the remarks while answering a question posed by Yemen's Arabic-language al-Masirah news agency on the sidelines of a conference held in Tehran on Monday, Press TV said in the report.
"If suitable conditions are provided, I would be ready to travel to Riyadh to settle differences" between the two countries, Zarif said.
"Tehran welcomes any initiative that aims to ease tensions in the region...," he added.
Zarif also said that he was in constant contact with Pakistani Prime Minister Imran Khan who made an official visit to Tehran earlier this month and held talks with Supreme Leader Ayatollah Ali Khamenei and President Hassan Rouhani.
In his meeting with Khan, Khamenei said a proper end to the ongoing war waged by Saudi Arabia and its allies on Yemen can have "positive" effects on the region, highlighting Iran's plan as a suitable solution to this crisis.
Tensions have been high between Iran and Saudi Arabia since the September 14 attacks that caused fires and damage to an oil processing facility and a production facility, The Express Tribune reported.
Saudi Arabia temporarily halted production at two Aramco oil facilities, interrupting about half of the company's total output - shutting down 5.7 million barrels per day of production - more than 5 per cent of global oil supply.
The attack was claimed by the Yemeni Houthi rebels, although the US and Saudi Arabia blamed Iran for it, an allegation which has been strongly denied by Tehran.
( With inputs from IANS )