The talks will occur on the sidelines of a UN General Assembly in New York. They come as Western powers seek to build support for the fight against the Islamic State (IS) jihadist group, which holds swathes of territory in Iraq and Syria and which has beheaded two US journalists and a British aid worker.
The United States and Arab allies launched the first air and sea strikes against IS militants in Syria today, expanding action against the jihadists the US has been leading in Iraq since the start of August.
Iran, which usually rails against any US presence in the Middle East, has been unusually accepting of the US action in Iraq, where it is also tackling IS militants.
Rouhani has criticised the US for not sending in ground troops, and on Monday said the people in the region were "defending themselves... Against the terrorists" and that Iran would help.
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But Iran's supreme leader Ayatollah Ali Khamenei, whose regime staunchly supports the Syrian government, claims he rejected a US offer to join the international coalition against the IS.
"If Iran is willing to join the international community to defeat ISIL (another name for IS), then we will work with them on that," a Downing Street source quoted by British media said.
French President Francois Hollande was also set to meet Rouhani today.
France has joined the US in striking IS targets in Iraq, and Arab nations such as Saudi Arabia, Bahrain and Jordan joined in the aerial assault in Syria today.
Britain, though, has so far not participated in the US-led military action against the IS group.
Britain's defence ministry said today that "discussions were ongoing" about possible action against IS.
Britain's Defence Secretary Michael Fallon was in Saudi Arabia and Bahrain Monday and today to discuss international action against the militants, officials said.