"The Prime Minister will use a trip to India to try to persuade the New Delhi government to buy more than 100 Eurofighter jets after the French President left empty-handed this week," the Daily Mail reported ahead of Cameron's three-day official visit which begins tomorrow.
French contractor Dassault Aviation was chosen last year as the preferred bidder for the contract to supply Rafale jet fighters to the Indian Air Force under a USD 10-billion deal - a blow for the UK-German-Spanish-Italian consortium, which includes Britain's BAE Systems, which builds the Eurofighter.
But Hollande's hopes of signing a final contract came to nothing this week - despite him squeezing in a visit before Mr Cameron. The French premier also failed to secure any major trade deals, the British paper claimed.
"That has sparked hopes in Downing Street that Cameron can persuade the Indian authorities to rethink the deal and buy the Eurofighter instead," it said.
"Officials made clear that the Prime Minister wants to steal a march on Hollande, who has repeatedly clashed with Cameron," the paper said.
Cameron angered the French by offering to put out a "red carpet" for entrepreneurs fleeing Hollande's new 75 per cent top rate of tax, while the French government retaliated with the same offer for British businessmen if the UK quits the EU in the referendum Mr Cameron has offered.
Quoting a British government source, the Daily Mail said: "Hollande was in India this week and a deal has not been signed so we will want to find out from the Indians how their talks are progressing with the French."
A No 10 official added: "We respect the fact that the Indians have chosen their preferred bidder and are currently negotiating with the French. Of course, we will continue to promote Eurofighter as a great fast jet not just in India but around the world."
However Prime Minister Manmohan Singh last week said that "discussions on the Medium Multi-Role Combat Aircraft (MMRCA) (Rafale) contract are progressing well."
Cameron will lead the largest ever trade delegation of ministers and businessmen to India, designed to strike defence, energy and education deals with the emerging superpower, the paper said.