A couple of Indian financial services companies have also shown interest in buying the wealth management business, and a formal bidding process is expected to start soon, a source told Reuters.
Morgan Stanley launched the sale of its Indian private wealth management unit in November last year after entering the fragmented and competitive market about four years ago.
The wealth management unit has approximately $1bn under management.
Standard Chartered is listed in the UK and India, with strong name awareness in many emerging markets having launched late last year an Islamic version of its online banking platform, Straight2Bank which is available in the United Arab Emirates, Bangladesh, Bahrain, Pakistan and Malaysia.
But in August last year, Standard Chartered agreed to pay a $340m penalty to the New York State Department of Financial Services, in an embarrassing concession to accusations that it laundered money on behalf of Iran.