The report comes as Washington and Tehran try to revive a 2015 nuclear accord which Riyadh was opposed to and as the United States presses for an end to the Yemen conflict.
Senior Saudi and Iranian officials have held direct talks in a bid to repair relations between the two regional rivals, four years after they cut off diplomatic ties, the Financial Times reported, citing officials briefed on the discussions.
The first round of Saudi-Iranian talks took place in Baghdad on April 9, included discussions about attacks on Saudi Arabia by Yemen's Iran-aligned Houthi group and were positive, the FT report added, citing one of the officials.
Saudi authorities did not immediately respond to a Reuters request for comment, and Iranian officials were not immediately available for comment. The FT said a senior Saudi official denied any talks with Iran.
Iraq's prime minister visited Saudi Arabia late last month.
The report comes as Washington and Tehran try to revive a 2015 nuclear accord to which Riyadh had been opposed to and as the United States presses for an end to the Yemen conflict, seen in the region as a proxy war between Saudi Arabia and Iran.
Riyadh has called for a nuclear deal with stronger parameters and said Gulf Arab states should join any negotiations on the accord to ensure that this time it addresses Iran's missiles programme and its support for regional proxies.
Saudi Arabia and its allies supported former US President Donald Trump's decision in 2018 to breach the world powers' nuclear agreement and reimpose sanctions on Tehran, which responded by withdrawing from several restrictions on its nuclear activities.
A Saudi foreign ministry official told Reuters last week that confidence-building measures could pave the way for expanded talks with Gulf Arab participation.