Mr Jaishankar is also scheduled to meet Deputy Secretary of State John Sullivan.
The Jaishankar-Tillerson meeting is likely to give final touches to the PM Modi-Donald Trump meeting at the White House on Monday.
Mr Jaishankar, a former Indian ambassador to the US, has been playing a leading role in shaping the India-US relationship under the Modi government.
"We're looking forward to strengthening ties between the United States and India," State Department spokesperson Heather Nauert told reporters at her daily news conference.
"We have a lot of areas of mutual cooperation, fighting terrorism, we have a lot of people-to-people ties, strong people-to-people ties; so we're looking forward to that visit," she said.
PM Modi will meet US President Donald Trump on June 26. He will hold talks with Mr Trump on a range of issues, including terrorism and India's concerns over possible changes in H-1B visa rules.
India has time and again raised the issue of H-1B with the US authorities and asked them to liberalise the visa regime as Indian companies contribute significantly to the American economy.
The H-1B is a non-immigrant visa that allows US companies to employ foreign workers in speciality occupations that require theoretical or technical expertise in specialised fields. The technology companies depend on it to hire tens of thousands of employees each year.
Apart from ways to enhance trade and business cooperation, PM Modi and Mr Trump are expected to discuss defence ties.