Cook's visit, which follows a trip to China, comes at a crucial time as Apple looks for new growth markets after posting its first ever decline in iPhone sales, and as India has denied it permission to sell refurbished phones - a move seen as key to appealing to price-sensitive local consumers.
The visit is Cook's first to India as the head of the US technology company, one of the sources said.
It was not immediately clear whether he would discuss importing refurbished iPhones with Indian government officials.
Apart from meeting Modi, Cook will also hold meetings with employees and partners, the source said, adding he would fly to India on Tuesday.
The sources declined to be named as the plan is not public yet. Apple declined to provide details of Cook's schedule in India.
Cook is visiting China after announcing a $1 billion investment in Chinese ride-hailing app Didi Chuxing.
His visit there also comes at a time when Apple is facing some setbacks in its most important overseas market.
From weakening smartphone sales to the loss of an iPhone trademark dispute and the suspension of some of its online entertainment services, Apple has faced a flurry of challenges in China in recent weeks.
Cook planned to meet high-level Chinese government officials, a source familiar with the matter said this month.
In India, Apple is looking to set up its first retail outlet, as it only has about a 2 percent market share. But its sales there surged 56 percent in the first three months of this year, driven mainly by cheaper older-generation devices such as the iPhone 5s.
More than 100 million smartphones were sold in India last year and the market is expected to grow by 25 percent this year, making India one of the fastest growing smartphone markets in the world.
Since his election in 2014, Modi has courted US tech companies as part of his strategy to bring jobs to India.
He met Cook last year during a high-profile visit to Silicon Valley, which included a 'town hall' at Facebook headquarters with Mark Zuckerberg and a round table meeting with other CEOs including Google's Sundar Pichai and Microsoft's Satya Nadella.
© Thomson Reuters 2016
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