The helmer, who made it big with 'Elizabeth', will direct one of the last pieces of writing from the late Minghella - a segment of the urban ode 'New York, I Love You'.
According to Kapur, Minghella asked the helmer to carry out his vision shortly before going in for surgery two weeks ago.
"Two days before Anthony Minghella went in for an operation on a tumor they had just discovered, Anthony called me to see if I would direct a short he had written," News24.com quoted Kapur, as stating on his website.
"I will direct the film now - with Anthony in my heart and in presence of his soul," he added.
Other movie heavyweights involved in the project include Hollywood stars Scarlett Johansson and Natalie Portman, Indian-born director Mira Nair and Brett Ratner, director of the 'Rush Hour' series.
Minghella, best known for the Oscar-winning 1996 film 'The English Patient', died last week at the age of 54.