Chakrabarty has "requested to be relieved earlier than the scheduled (term ending June 15, 2014)," a top government source said.
Chakrabarty, 62, who was appointed as RBI Deputy Governor in 2009, could not be contacted as he was travelling.
The source, however, did not say why he has sought an early end to his term.
Chakrabarty was appointed as RBI Deputy Governor for a three-year term on June 15, 2009 and was subsequently given a two-year extension.
His extended term was to come to end on June 15, 2014.