The transaction will be similar to the $1.8 billion investment by Bain Capital in November 2017.
"The conversation has been ongoing for almost a month. The Axis stock has been volatile. The brass seems to be warming up to the idea of another deep-pocket marquee investor in recent weeks," the newspaper quoted a source as saying.
Moneycontrol could not independently verify the report.
Axis Bank and Carlyle declined to comment when approached by The Economic Times.
The capital raising might be done via a primary issuance of shares through a preferential allotment, following which Carlyle will own 5-8 percent of Axis Bank, the report said.
The transaction will be similar to the $1.8-billion investment by Bain Capital in November 2017.
The discussions are in the early stages and no formal sale process has begun, executives told the newspaper.Kotak Mahindra Bank on May 26 initiated a qualified institutional placement (QIP) to raise Rs 7,460.38 crore.