The Times of India said Ukrainian air traffic controllers had asked the Air India pilots to try and establish contact with the Malaysia Airlines jet, which had stopped responding to its calls.
The Air India plane, which was flying from Delhi to Birmingham and was less than 25 kilometres from Malaysia MH17, received no response, according to the paper.
"The AI Dreamliner was less than 25km from the Malaysian aircraft when the latter was hit by a missile," an unidentified airline source told the newspaper. According to Times of India, a distance of 25km can be covered in 90 seconds by a Dreamliner aircraft.
"When the pilots learned of the cause of the crash later, they were stunned."
According to the newspaper, it is standard practice for air traffic controllers to ask pilots of aircraft in the vicinity to get in touch with pilots who have stopped responding.
The newspaper also said that minutes before the crash, the Air India pilots heard air traffic controllers give the Malaysian plane a "direct routing".
This allows a plane to fly straight rather than tracking from one navigation point to another, and saves time and fuel.
An Air India spokesman declined to comment on the report.
The report comes despite a denial by India's civil aviation ministry last week that the Air India plane was close to the Malaysian jet, which was cut down over Ukraine's troubled eastern region on Thursday.
Ukraine accuses Moscow of helping pro-Russian rebels to shoot down the Malaysian plane, killing 298 people.