The International Monetary Fund is looking at alternatives to realign quotas that will put India into the top 10 shareholders, she said.
"Implementing the reform would lift up India within the top 10 shareholders of the institution. It's hard work because there is one member which is not ratifying. The US that was determined to re-balance, to move Europeans out and bring emerging market economies in, is not ratifying the reform," she said at a lecture at Lady Sri Ram College.
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IMF, she said, is "looking at options... I hope some would be acted upon. I certainly hope so. But we need to (bring) comprehensive reforms...So that economies are represented in a fair manner."
Quota reforms seek to provide greater say to developing economies in the IMF.
She emphasised that IMF is a global multilateral institution where countries like India must have bigger say.
The ratification of the US is necessary to implement the quota reforms, agreed by the member countries in 2010.
"It so happens when IMF was set up 70 years ago, there was a very large economy which is still the first economy in the world, the US, that had the veto right. That is in the Article of constitution. So major changes such as representation around the table can only happen with approval of the US which has about 15 per cent voting right," Lagarde said.
It would be in the interest of everybody to implement 2010 reforms, she added.
India has quota of 2.44 per cent, with 2.34 per cent voting right in the IMF.
As per the current quota system, the US has 17.69 per cent while the voting right is 16.75 per cent. It is followed by Japan - 6.56 per cent with 6.23 per cent voting share.
Highlighting the importance of India, Lagarde said 'the world needs a vibrant India and India needs the world'.
"As one of the largest commodity importers in the world, an open and transparent multilateral system for trade and financial flows will be essential to support India's vibrant economy. With growing economic size and power come greater leadership expectations," she said.
"We look forward to seeing India becoming even more active on the global stage - in fora such as the G-20 and the IMF," she said.