The newspaper -- owned by News International Ltd., the main British subsidiary of News Corp., which also owns "Slumdog" distributor Fox Searchlight Pictures -- said the deal was allegedly offered to one of its reporters.
The father, Rafiq Qureshi, has denied any wrongdoing.
The accusations further complicated the lives of the families of the slum-dwelling child stars, who have come under intense scrutiny since the movie skyrocketed to Oscar-winning fame and grossed more than $300 million worldwide.
"There is not any crime. The matter is closed," said Rahim Shaikh, the senior police inspector in Mumbai's Nirmal Nagar, where the claim against Qureshi was processed.
No charges have been filed, he added.
Police questioned Qureshi but were unable to track down the three journalists who carried out the alleged sting.
Officers looked for them at the Leela, a five-star hotel where the report said they met Qureshi but they had already left, Shaikh said.
Police traced two mobile phone numbers the trio gave the hotel to local Vodafone SIM cards, which were activated on April 16 and deactivated on April 19.
Indian police made no further efforts to contact the journalists or News of the World in England, Shaikh added.
"The matter is closed. No money changed hands. Rubina is here. There is no crime," he said.
After the report, Rubina's estranged mother thanked News of the World "for bringing this matter to light."
"You have come like angels for me and my daughter and saved her from ending up God knows where," she told the paper. "Who knows who Rubina would have been sold to, or what would have happened to my child if you hadn't exposed Rafiq."
Dewade could not be reached for comment Thursday.
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