The deal by Reliance with UTV Software, in which Disney controls 50.44 percent, is expected to be completed in the coming weeks, the newspaper said late on Sunday, citing people close to the development.
UTV Software said it had no immediately comment on the report, while Reliance could not be immediately reached.
Reliance, which has diversified into telecom, retail, financial services and hospitality sectors in recent years from its core business of refining and oil and gas exploration, last year acquired Infotel, which emerged as the only firm to secure nationwide wireless broadband radio airwaves in an auction.
The deal is expected to give Reliance access to games, entertainment and children's content for their telecom operations, the paper said.
Reliance has plans of building a data-focused business which will provide mobile, smartphone, tablet and computer users access to the net and online related services via a wireless broadband network.
The diversified company, which has been under pressure from falling gas output, has pushed for tie-ups in recent months to boost its business.
In June, Reliance signed a joint venture with DE Shaw, a U.S. hedge fund, for acquiring Bharti Enterprises 74 percent stake in an insurance joint venture with France's Axa.
The following month the Indian cabinet approved Reliance's plan to sell a stake in 21 of 23 planned oil and gas blocks to BP as part of a $7.2 billion deal.
At 10:24 a.m. (0454 GMT), shares in Reliance, valued at $53.5 billion, were up 1.5 percent at 815 rupees in a firm Mumbai market.
The stock has been a laggard, falling 24 percent in the year to date compared with a 21 percent drop in the main index, largely due to falling gas output.