Korati is waiting for board approval for the move, according to The Economic Times of India.
The former Global Steel director was named acting CEO of Axis in March last year after managing director and CEO Alok Gupta quit the firm for personal reasons.
Korati joined Axis in 2007, rising to executive director before being given the top job.
He was previously a managing director for the $355m Asia Equity Infrastructure Fund.
IL&FS is one of the largest and oldest private equity fund managers in India with more than $3.2bn under management, according to its website.
Its current investments include department store chain Shoppers Stop, the Noida Toll Bridge Company and Gujarat Pipavav Port.
Copyright © 2012 AltAssets