As asked on Quora, they all made some pretty good points there, &and ever since then there wasn't any new information that came to light.
But what was that role? While watching the movie I didn't notice any Indian ethnicity role there. What role was Irrfan supposed to play?
One of the posters in Quora even mentioned about the possibility of the role being Doyle's, played by Wes Bentley
In another article,
He was also asked to be a part of Christopher Nolan’s Interstellar which he turned down because he didn't want to let go of The Lunchbox and D-Day, two Hindi films he had already made a commitment to. Rumours suggest he was offered the role of Matt Damon or David Gyasi in the film.