The two companies will make six films a year for the next six years under the 1.5 billion dollar deal, The Times of India said, quoting an unnamed Reliance executive.
Reliance officials were not immediately available for comment.
A deal with Spielberg -- the highest-grossing film director ever -- would raise Mumbai-based Reliance-ADA's growing global profile in the entertainment industry.
It would also give Spielberg a financial boost in his efforts to secure DreamWorks' exit from Viacom Inc's Paramount Pictures and make it a company that again owns the films it makes.
There has been widespread speculation that the two companies were working on a deal.
Paramount Pictures this week congratulated Spielberg and his Dreamworks colleagues on their "newest venture" -- even though no announcement had been made.
US reports have said Spielberg aims to raise more than one billion dollars in third-party financing to reinvent DreamWorks as a separate company.
DreamWorks, which could not be reached for comment, makes live action films, such as "Transformers" and "Saving Private Ryan," and animated movies such as "Shrek" and its latest hit, "Kung Fu Panda."
In May, Reliance-ADA's entertainment arm, Reliance Big Entertainment, said it had signed deals with the production houses of Hollywood stars including Brad Pitt and George Clooney to make movies worth about a billion dollars over two years.