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 Ansar Allah (Houthi movement) and were positive, the FT report added, citing one of the officials.
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 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.
Saudi Arabia and its allies supported former U.S. President Donald Trump's decision in 2018 to quit the world powers' nuclear agreement and reimpose sanctions on Tehran.
A Saudi foreign ministry official told Reuters last week that confidence-building measures could pave the way for expanded talks with Persian Gulf Arab participation.
According to other sources, both Iranian and Saudi officials today has denied any direct talks between two countries.