"A new governor will be named after Prime Minister returns from his Africa tour on July 11," the official said.
Rajan's three-year term will come to an end on September 4, as he last month announced that he would return to academia and not seek a second term.
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Gokarn is an Executive Director at the International Monetary Fund, a post previously held by Mohan.
Others who are said to be in the fray for job include SBI chief Arundhati Bhattacharya and Economic Affairs Secretary Shaktikanta Das.
Government's Chief Economic Adviser Arvind Subramanian and the RBI's current Deputy Governor Urjit Patel are also considered to be in reckoning.
Incidentally, Patel got a three-year extension as RBI Deputy Governor in January.
Traditionally, Prime Minister picks the RBI Governor after consultation with the finance minister. The same process is likely to be followed this time around with Modi choosing Rajan's successor after consulting Arun Jaitley.
Sources said once a new governor is named, he will become an Officer on Special Duty (OSD) in the central bank to allow smooth transition.
Rajan, who will have the shortest tenure as RBI Governor since liberilsation began in 1991, decided not to seek a second term after unbridled political attacks on him was led by BJP MP Subramanian Swamy.
All RBI Governors in past 23 years have got second term - from Dr C Rangarajan (1992-97), Bimal Jalan (1997-03), YV Reddy (2003-08) to D Subbarao (2003-08). Rajan will break that chain.
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