The model code of conduct has come into force with the announcement of poll dates on Wednesday.
"My sense is if all goes well, we should be able to do it (issue new licences) in a few weeks," Rajan said, adding that the RBI would approach the Election Commission to ensure there is no violation of the model code of conduct.
Last month, the Bimal Jalan panel, which scrutinized applications for new bank licences, submitted its report to the Reserve Bank of India.
The central bank chief said it is doing a due diligence on the applicants for the new banking licence.
About 25 players in the fray for bank licences. Public sector units India Post and IFCI and private players such as Anil Ambani group and Aditya Birla group are among the applicants. Bajaj Finance, Muthoot Finance, Religare Enterprises and Shriram Capital have also applied.