Mr Trump and Mr Modi are said to have a warm relationship, something that has been helped by the Indian leader being invited to the Oval Office on several occasions and the Trump administration’s recent criticism of India’ neighbour, Pakistan.
But in a development that could cause tension between the two countries, a new report claims Mr Trump, who earlier this month triggered controversy when it was reported he used the phrase ’s***hole” countries when referring to Haiti and African nations, reportedly imitates the Indian leader’s accent.
The Washington Post reported Mr Trump’s behaviour in the context of the US’s provision of additional troops to Afghanistan, where it is supposed to have adopted a non-combat role.
It said Mr Trump imitated the accent of Mr Modi, who can speak and understand English but prefers to converse in his native Hindi, and claimed that he said to him: “Never has a country given so much away for so little in return” - as the United States in Afghanistan.
Mr Trump claimed the Indian leader’s comment was was proof the rest of the world viewed the United States as being taken advantage of in Afghanistan.
Both the White House and State Department failed to respond to questions about the claim. Indian officials in Washington also did not immediately respond.
If true, it would not be the first time Mr Trump had adopted a fake Indian accent. In the spring of 2016, during the election campaign, Mr Trump used a such a voice to mock a call centre representative in India.
The New York billionaire claimed he called up his credit card company to find out whether their customer support is based in the US or overseas.
“Guess what, you’re talking to a person from India. How the hell does that work?” he told his supporters in Delaware.
“So I called up, under the guise I’m checking on my card, I said, ‘Where are you from?’
“‘We are from India’,” said Mr Trump, impersonating the response he claimed to have received. “Oh great, that's wonderful. India is great place. I am not upset with other leaders. I am upset with our leaders for being so stupid.”
Mr Modi and Mr Trump may be set for a potentially awkward meeting this week at the World Economic Forum in Davos. The forum will open on Tuesday with a speech by Mr Modi and end on Friday, when Mr Trump is due to address the large auditorium where Chinese President Xi Jinping spoke last year.