The visit, if it happens, will be Cook's first to India as the head of the US technology company. It was not immediately clear whether he would discuss importing refurbished iPhones with officials in New Delhi.
Apple Inc Chief Executive Tim Cook will visit India this week and meet Prime Minister Narendra Modi on the second leg of his Asian tour, two sources familiar with the matter said, as the company seeks to revive sluggish iPhone sales.
Cook's visit, following 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 officials in New Delhi.
A second source said India was keen to know if Apple had plans to set up production facilities for the local market, which would be a boost for Modi's "Make in India" manufacturing push.
"If they can make in China to cater to the Chinese market then they can make for Indian markets here," said the source.
Maharashtra, also run by Modi's Bharatiya Janata Party, is already in talks with Apple product maker Foxconn Technology over it setting up an iPhone plant there.
Apart from meeting Modi, probably on Tuesday, Cook will also meet employees and partners, the sources said.
The sources declined to be named as the plan is not public. 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 comes at a time when Apple is facing some challenges in its most important overseas market, including weakening smartphone sales, the loss of an iPhone trademark dispute and the suspension of some of its online entertainment services.
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 U.S. tech companies as part of his strategy to bring jobs to India. He met Cook last year during a visit to Silicon Valley.