This follows Bharti Airtel, which was in "exploratory" talks with the South African company, pulling out of the deal.
According to sources, RCom has formally approached MTN Group on Thursday and the company has started discussions for a possible takeover.
When contacted, an RCom spokesperson declined to comment.
This is the second attempt by RCom to acquire MTN Group, as earlier last year the company had initiated talks with the South African company. RCom chairman Anil Ambani had met MTN Chief Executive Officer Phuthuma Nhleko last year, even though the talks were not "successful".