Rao, 60, is currently in Islamabad for the latest round of peace talks with her Pakistani counterpart Salman Bashir.
The foreign ministry declined to confirm the appointment, but the Press Trust of India cited official sources as saying the posting had been cleared by the government and a formal announcement was "expected soon".
Ending a freeze of over two years, India and Pakistan announced that peace talks would resume after a meeting between Rao and Bashir in February.
Rao has already served in several high-profile ambassadorial postings, including China.
Relations between Delhi and Washington, characterised by mistrust and occasional hostility during the Cold War, were reset by former US president Bill Clinton in the 1990s and invigorated by his successor George W. Bush.
President Barack Obama visited last November as part of an Asian tour that reflected the rapid growth in India's economy and a shift in power to emerging nations as a result of the global financial crisis.
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