Strategists in Modi's Bharatiya Janata Party (BJP), confident that his jobs-first policy pitch will secure a strong voter mandate, suggest that they would prefer to have one of their own at the helm of the Reserve Bank of India (RBI).
That sets the stage for a confrontation with Rajan, who since being appointed last September has enjoyed an unusually smooth ride in a country where governments often treat the RBI as a punchbag for their own policy failings.
The former International Monetary Fund chief economist is widely viewed as India's most capable technocrat, winning the respect of investors for his handling of a currency crisis that hit Asia's third-largest economy last year.
"It will be a big loss of face for the country and would create a negative perception among foreign investors if the BJP removes the governor immediately after forming the government," said A Prasanna, an economist at ICICI Securities Primary Dealership Ltd in Mumbai.
Before moving to the RBI, Rajan, 51, served as chief economic adviser to the finance ministry under the Congress party-led government, which opinion polls say faces defeat in the five-week national election starting on Monday.
BJP treasurer Piyush Goyal has attacked Rajan over a series of interest rate hikes intended to curb inflation, now running at double the RBI's longer-term 4% target, at a time when economic growth has fallen to its slowest in a decade.
Rajan has raised the repo policy rate three times by a total of 75 basis points to 8%.
"Governor Rajan is only aggravating the problems and making them worse by increasing interest rates," Goyal, a leading strategist and fundraiser for the nationalist opposition party, told the Economic Times.
Subramanian Swami, a BJP ideologue and former cabinet minister with close ties to a Hindu grassroots movement that has shaped Modi's thinking, puts it more bluntly: "We can make it worthwhile for him to leave," Swami told Reuters.
"I would not be surprised if a government led by Narendra Modi removes the governor," said Satish Misra, an analyst at the Observer Research Foundation, a Delhi-based think-tank. "Modi does not brook any opposition."
GOOD COP, BAD COP
Rajan's policy and academic credentials - he was a professor at Chicago's Booth School of Business - qualify him as a card-carrying member of the policy jetset that gathers twice a year at the IMF's Washington headquarters or at Group of 20 meetings.
Yet his autonomy as central bank governor is more circumscribed than that of his counterparts in the West, who are typically nominated by the government but also accountable to lawmakers.
Under the RBI Act of 1934, Rajan serves at the pleasure of the government: "The central government may remove from office the Governor, a Deputy Governor or any other Director," it says.
While no RBI governor has been sacked in the central bank's 80-year history, two have quit before completing their terms - most recently Sir Benegal Rama Rau, who resigned in 1957 due to differences with the finance minister.
In that context, analysts interpret the verbal broadsides as a softening-up exercise intended to secure greater RBI compliance with Modi's expansionist credo.
To be sure, Rajan has moderated his rhetoric on inflation but analysts said that is more a response to cooler inflation than anything else.
Arun Jaitley, a BJP leader tipped to assume either the finance or home affairs portfolio in the next government, has meanwhile avoided confrontation. Asked about Rajan in a TV interview last month, Jaitley said: "If someone is doing good job, he will certainly continue."
Manufacturers and traders, a constituency of the right-wing BJP, have complained that the RBI under Rajan has allowed the rupee to recover too strongly with a near 15% rally from last year's slump, hurting India's export competitiveness.
The Confederation of Indian Industries (CII) has called for a cut in interest rates of 100 basis points and a more competitive exchange rate to support domestic manufacturers.
Rajan's former colleagues at the finance ministry say he is a pragmatic and politically savvy economist who may yet find a way to work with a BJP-led coalition government that pundits say is most likely to be formed after votes are tallied on May 16.
For his part, Rajan cautions that coalition building may not go as smoothly as bullish foreign investors may expect. They have bought $10 billion in Indian stocks and bonds this year, driving the BSE Sensex to record highs.
Speaking on Tuesday after the RBI kept its key rate unchanged, Rajan cautioned that "we have to be prepared for some turmoil" in the event that the next government is not stable.
As long as the next government shows proper concern about the economy and the fiscal situation, Rajan added, "I would suspect that after an initial bout of turmoil there might be a reassessment which may be more positive".
Those statements represent a careful deployment by Rajan of his credibility with markets to guard against any attempt by a BJP-led government to render his position untenable.
"It would not be easy to remove Rajan from a constitutional post," said a senior finance ministry official, who spoke on condition of anonymity. Explaining why, he used the same words as Rajan: "It would lead to turmoil in the markets."