The incident involving Emirates and Etihad Airways was reported to the Directorate General of Civil Aviation, which has started its investigation, the sources said.
While Emirates confirmed the incident in a statement from Dubai, Etihad when contacted said it will respond soon.
The incident occured on the intervening night of March 29-30, when Emirates flight EK-706 was heading to Dubai from Seychelles while Etihad flight EY-622 was on way to Seychelles from Abu Dhabi, the sources said.
An RA is given to the pilot if the distance reduces to the extent that the risk of collision gets to 25 seconds.
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It is an indication given to the flight crew recommending either a manoeuvre intended to provide separation from all threats; or a manoeuvre restriction intended to maintain existing separation.
This is also an instruction to climb, descend or level out. The pilot is required to comply in 6 seconds, the instruction has priority over other ATC instructions.
The crew informed the authorities of the incident and later filed an Air Safety Report, which will be forwarded to Mumbai Air Traffic Control, the spokesperson said.
Safety is of paramount importance to Emirates and "we will be cooperating fully with the Mumbai Air Traffic Control in the subsequent investigation," the airline added.
Due to the closure of Yemeni airspace in the wake of the on-going civil war in the region, Emirates and Etihad are operating to Seychelles using Mumbai and Muscat airspace.