The meeting, the first at a high level to discuss the expansion, will take place on Tuesday during Modi's state visit to the United States, said the source, who declined to be named as the discussions will be private.
Executives of the U.S. automaker visited India and held talks with Indian bureaucrats and ministers last month on establishing a manufacturing base for cars, and also to make batteries in India.
Musk will discuss investment plans and outlook with Modi, the source said, describing the planned discussion as a "high-level meeting about India's economic potential".
"Tesla has very strong plans for India, including looking at manufacturing," the person added.
Tesla did not respond to Reuters queries. An Indian government spokesperson did not respond to a request made outside of business hours.
Musk said last month Tesla would probably pick a location for a new factory by the end of this year, adding India was an interesting place for a new plant.
U.S. companies like Tesla and Apple face challenges of reducing reliance on China as a manufacturing base in the face of tensions between Washington and Beijing.
Tesla last year shelved its India entry plans due to high import tax structures, but has renewed talks in recent weeks by sharing plans with Indian officials about a manufacturing base there, which India has long sought.
Modi's meeting with Musk, who owns Twitter, will assume greater significance as it comes days after Twitter co-founder Jack Dorsey accused India of threatening to shut down the platform for not complying with content takedown orders during a 2020-2021 protest. India called the allegation an "outright lie".
Musk has not commented on the episode, which caused a political storm in India.
Musk said at an event on Friday, "I'm generally a fan of that we should have free speech as much as possible, as much as is allowed by the laws of any country."
Meanwhile, Tesla shares went up 4% after Reuters first reported Rivian (RIVN.O) would adopt Tesla's electric vehicle charging standard.
