The firm, which owns, operates and manages hotels, palaces and resorts, is likely to hive-off the two properties into separate entities.
While the foreign investor may pick up 74 per cent interest in the hived-off entities, Leelaventure will retain 26 per cent stake and continue to manage the five-star hotels, industry sources said.
The deal is however not yet finalised, they said.
A Leelaventure spokesperson did not reply to emails seeking comments.
When it was first reported in February that Leelaventure is selling the two hotels, the company informed the stock exchanges: "In terms of Corporate Debt Restructuring (CDR) package being implemented, the company has to reduce its debts through sale of assets."
It had stated that the company was "in discussion with various investors" and it continues to "evaluate proposals".
Sources said as part of discussions with the cash-rich sovereign wealth funds of Abu Dhabi, Qatar and Malaysia, Hotel Leelaventure will still run and manage the Delhi and Chennai properties for 33 years for a fixed fee.
The Leela chain, in which ITC Hotels holds 12 per cent stake, has been in the red for the past several quarters, hit by business slump, competition and demand-supply mismatch.
Part of The Leela Group, The Leela Ventures is looking to divest stakes in its bouquet, full of luxury hotels, resort properties, IT and business parks, as well as real estate development.
In 2011, it sold the luxury Kovalam beach hotel to industrialist Ravi Pillai for Rs 500 crore and followed it up by selling the Chennai IT park building for Rs 170.17 crore to Reliance Industries in 2012.
Sources said it is now in talks to offload stakes in The Leela Palace, Delhi and The Leela Palace, Chennai to pare debt after moving the corporate debt restructuring (CDR) cell.
CDR is a mechanism where borrowers seek extension of loan period and adjustment of interest rate. Hotel Leelaventure's debt as on September 30, 2013 was Rs 4,295.15 crore.
Sources said IDBI Capital and SBI are advising Leela on the transaction.
Leela Delhi is a 260-room property in the heart of the capital for which the group had paid nearly Rs 600 crore for buying land. Located in the diplomatic enclave at Chanakyapuri, it is the capital's first freehold property.
Leela Chennai is a 326-key property on the sea face in Chennai's MRC Nagar.