Jaishankar is also scheduled to meet Deputy Secretary of State John Sullivan.
The Jaishankar-Tillerson meeting is likely to give final touches to the Modi-Trump meeting at the White House on Monday.
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.
After Trump won the presidential elections last November, the two leaders have spoken over phone three times, the last being Trump's congratulatory phone call after the BJP won the Uttar Pradesh Assembly elections.
Modi will meet US President Donald Trump on June 26. He will hold talks with 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.
Apart from ways to enhance trade and business cooperation, Modi and Trump are expected to discuss defence ties.
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