Bangladesh's Foreign Secretary Shahidul Haque is said to have conveyed this to his counterpart S Jaishankar while he was in New Delhi to attend the World Economic Forum meeting.
"We can help the Myanmar Government, but solution can't be their stay in Bangladesh".
Suu Kyi, who has been severely criticised for her failure to curb the military crackdown, said last month that Myanmar would take back "verified" refugees.
He added that the two nations had agreed to set up a joint working group to coordinate repatriation.
He did not give further details about the process.
Over-burdened with over half a million Rohingya refugees from Myanmar seeking shelter in Bangladesh, the country's Foreign Secretary, Shahidul Haque on Friday said that the immigration of the minority Muslims from the Buddhist-dominated country can not end the on-going crisis.
Rights groups say the real death toll is likely to be much higher, especially among the Rohingya, while the United Nations has labelled army operations as "ethnic cleansing" against the Muslim group.
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Prominent human rights groups have reported documented cases of systematic attacks by the Myanmar military and Buddhist extremists against Rakhine's Muslim population, including random shootings, rape and arson attacks.
Prior to the Monday talks in Dhaka, Bangladeshi Prime Minister Sheikh Hasina had demanded an immediate end to violence and safe passage in Myanmar for the refugees to return to their ancestral homes.
The Rohingya, a stateless mostly Muslim ethnic minority, have long faced persecution in Rakhine in northern Myanmar (Burma). We call for implementation of recommendations of the (Kofi Annan-led) International Rakhine Advisory Commission to tackle the root cause of this crisis.
The stress on Bangladesh has been increasing as the inflow of refugees continues even after nearly more than 40 days after the first instance of violence on 25 August.
Around 500,000 Rohingya people have fled the state of Rakhine, to seek shelter in Bangladesh.
Global aid groups fear tens of thousands of Rohingya Muslims who remain in northern parts of Rakhine are in urgent need of food, medicine and shelter after over a month of military operations.
Health experts have also voiced alarm that conditions in the grossly deficient camps are ripe for disease outbreaks such as cholera.
On a one-day visit organised by Myanmar authorities, United Nations officials, diplomats and aid groups were flown by helicopter to Maungdaw, epicentre of the violence.