But the Walla News website said he would discuss Iran's nuclear programme and its activities in the region with both Bennett and his Israeli counterpart David Barnea.
Burns will also travel to Ramallah in the Israeli-occupied West Bank for talks with Palestinian president Mahmud Abbas, a Palestinian official said.
His visit comes amid what analysts have called a "shadow war", that has seen a spate of attacks on vessels linked to Iran and Israel.
Last month, the MT Mercer Street, an oil products tanker operated by Israeli-controlled Zodiac maritime, was struck by a drone off the Omani coast, killing two crew members -- a Briton and a Romanian.
G7 foreign ministers on Friday pointed the finger of blame for the attack at Iran, as the US military released the findings of an investigation alleging the drones were made in the Islamic republic.
Iran dismissed the allegations.
A career diplomat, Burns played a key role in the US rapprochement with Iran that led to a 2015 nuclear deal between Iran and major powers.
With strong support from Israel, then president Donald Trump abandoned the agreement in 2018 and reimposed punishing sanctions on Iran.
But his successor Joe Biden's administration has held multiple rounds of indirect talks with Iran on returning to the deal.