"With critical negotiations between the Reserve Bank and North Block over the composition of the new interest rate-setting Monetary Policy Committee (MPC) still underway, a 0.25 per cent rate cut could judiciously help lubricate these discussions at little potential macroeconomic cost," the brokerage said in a note.
It can be noted that after adopting formal inflation targeting, the Finance Ministry and the RBI are in discussions on the composition of the five-member MPC that will be deciding the key issue of interest rates.
The note by BNP Paribas said this is Rajan's final chance to deliver the cut as the factors influencing it will only get difficult with time.
"The RBI has an opportunity to deliver a third, but likely final, 25 basis points cut in the repo rate on June," it said, adding the factors like threat of inflation fanning up due to a likely bad monsoon and the climbing oil prices, and the expected hike by US Fed in September which can lead to choppiness in the markets, can make it tougher to cut later.
On the transmission, it said Rajan has a choice to either "admit to impotence or try harder to spark transmission."
Only a few banks, led by State Bank of India, have cut their key rates after being chided by Rajan for not passing the 0.50 per cent cuts to borrowers in two surprise installments in January and March.