Bangladesh leader Sheikh Hasina met National Security Advisor Ajit Doval Monday evening after landing at the Hindon Air Force base in Uttar Pradesh's Ghaziabad - around 30 km from Delhi.
Prime Minister Narendra Modi has been briefed on the situation in Bangladesh by External Affairs Minister S Jaishankar. There is no word yet if Mr Modi will meet Mrs Hasina.
Congress MP Rahul Gandhi, who is the Leader of the Opposition in the Lok Sabha, has also spoken to Mr Jaishankar. The two spoke briefly on the sidelines of the Parliament, his party said.
Hours earlier the 76-year-old five-time Prime Minister had been forced to resign from her position after more than 300 people died in violent protests over a quota for government jobs in that country.
Sheikh Hasina is expected to leave for London later, sources told NDTV, where she may seek political asylum. Sources told news agency ANI Sheikh Hasina's plane - a Bangladesh Air Force C-130 military transport - will be parked near the Indian Air Force's C-17 and C-130J Super Hercules aircraft hangars.
Sources said Mrs Hasina's plane is being refuelled for the flight to London.
India's Border Security Force is on high alert across the country's 4,096 km border with Bangladesh, with field commanders ordered to take "on ground" positions and be prepared for anything.
