No further details regarding the purported deal have been made public yet.
Trump was speaking at an event with business leaders in Doha where he announced a series of deals between the US and Qatar, including for Boeing jets.
According to Bloomberg, the US president also said he had told Apple CEO Tim Cook not to expand production in India.
"I said I don't want you building in India," Bloomberg quoted Trump as saying about a conversation he said he had with Mr Cook. He added that Apple would be "upping their production in the United States".
In an earnings call earlier this month, Apple had said it was shifting production of most iPhones from China to India while Vietnam would be a major production hub for items such as iPads and Apple watches.
President Trump slapped tariffs of up to 27% on Indian goods in April. Delhi is rushing to negotiate a trade deal during Trump's 90-day pause on higher tariffs, which ends on 9 July.
The US was until recently India's biggest trading partner, with bilateral trade amounting to $190bn (£143bn).
Delhi has already lowered tariffs on Bourbon whiskey, motorcycles and some other US products, but the US has a $45bn trade deficit with India, which Trump wants to reduce.
"As Trump always blamed India's high tariffs for the trade deficit, India could offer to make 90% of US exports tariff-free from day one, using a "zero-for-zero" approach - cutting tariffs on all goods except autos and agriculture. But the deal must ensure strict reciprocity, with both sides eliminating tariffs equally," says Ajay Srivastava, a Delhi-based trade expert.
Trump and Modi have set a target to more than double trade to $500bn, but Delhi is unlikely to offer concessions in sectors such as agriculture where there are deeper political sensitivities involved.
India has recently shown more openness to doing trade deals after years of scepticism.
Last week, it inked a trade pact with the UK that will substantially slash duties in many protected sectors like whisky and automobiles.
India also signed a $100bn free trade agreement with the European Free Trade Association (EFTA) last year - a group of four European countries that are not members of the European Union - after almost 16 years of negotiations.
EU and India are also pushing to get a free trade agreement done this year.
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