All but three of the 52 economists polled last month predicted the RBI would keep India's policy repo rate on hold at 8 percent on Tuesday, after last raising interest rates by a quarter percentage point in January.
The decision is expected at 0530 GMT Tuesday.
Rajan is already showing some success in bringing down consumer price inflation (CPI) after raising interest rates by a total of 75 basis points since September, and analysts widely expect price pressures to keep moderating by early 2015 as the government battles market inefficiencies which raise costs.
The governor will now have to sell his agenda - which puts priority on the fight against inflation - to India's new prime minister, Narendra Modi, who many count on to push up the growth rate.
Investors are hopeful the new government will respond to Rajan by tackling the supply-side factors that drive up food inflation in India, thus easing the burden on the poor and restoring investors' confidence.
"There is a realisation in the new government that high inflation is politically costly, and so they will be willing to walk the extra mile to bring down inflation," said A. Prasanna, economist at ICICI Securities Primary Dealership in Mumbai.
Rajan started toning down some of his anti-inflation rhetoric on expectations of easing retail inflation, which except for an increase in April to 8.59 percent, has been cooling in 2014. It was nearly 10 percent throughout the two previous years.
Last week, after meeting new Finance Minister Arun Jaitley, the central bank governor told reporters of the importance of balancing growth and inflation. He later told a Tokyo audience he would work hand-in-hand with the government.
The RBI is targeting to bring down CPI inflation to 8 percent by January 2015 and 6 percent the following year, in line with recommendations from a central bank panel in January.
Most analysts expect the RBI to keep interest rates on hold through 2014 unless India experiences a sudden spurt in inflation, which could happen if there are reduced rains during the monsoon season.
Yet to bring down inflation, the RBI will need the new government to also take steps to bring down food inflation as well as contain its elevated fiscal deficit.
Modi is expected to soon unveil a roadmap to tame food prices, control the fiscal deficit and push reforms to boost Asia's third largest economy, which posted its second straight year of sub-5 percent growth in the year ended in March.
The RBI will also need to work with the new government in making other important decisions, including whether to remove restrictions on gold imports that have sharply narrowed the current-account deficit but are believed to have spurred in increase in smuggling.
In turn, Rajan is likely to help the government fulfill parts of its agenda, including most prominently by ensuring that enough cash is available for infrastructure projects.
Rajan hinted last month the RBI could consider freeing up some banks from meeting hefty reserve requirements and promised support for the sale of infrastructure-related bonds.