"If it is in my control, I will continue with him. He is a good economist. Till now he has proven himself as a good governor and he should continue," he told Focus TV.
Sinha's statement comes in the backdrop of speculation that the RBI Governor could be changed if the Narendra Modi-led NDA comes to power after the general elections. The nine-phase election is under way and counting of votes is scheduled on May 16.
Rajan, a career economist, was appointed by the UPA government and assumed charge at the RBI on September 4, 2013.
He was earlier the Eric J. Gleacher Distinguished Service Professor of Finance at the University of Chicago's Booth School. Between 2003 and 2006, Rajan was Chief Economist and Director of Research at the International Monetary Fund.
On noted economists Jagdish Bhagwati and Arvind Panagariya showing interest in playing some role if a Modi-led government is formed, Sinha said, "Both are world-class economists and any kind of help from them will be welcomed."
Replying to a question on reducing import duty on gold, he said: "The gold business, which is a source of employment for lakhs of people, has been ruined. We need to change the system."
Asked who could be the finance minister in an NDA government if the coalition wins, Sinha said it will depend on the Prime Minister.
However, he said "it will be good if a person with knowledge of economics becomes finance minister."