"We want to finalise the deal at the earliest," Sunil Barthwal, India's commerce secretary, told reporters on Friday.
He said that on almost all contentious issues, negotiations were completed, and the deal could be signed "much before" the end of the year.
New Delhi sees an FTA with Britain as crucial to hopes of becoming a bigger exporter, while the UK would obtain wider access for its whisky, premium cars and legal services.
For India, an FTA with the UK would be its first with a developed country after it signed an interim trade pact with Australia last year.
For Britain, it is part of a quest for diversified global trade relationships after its 2020 exit from the European Union.
"While we’ve made good progress in closing chapters, we’re now focused on the high ambition areas including goods, services, and investment," a spokesperson for Britain's Department for Business and Trade said.
"We are clear that we will only sign when we have a deal that is fair, balanced, and ultimately in the best interests of the British people and the economy."
It comes at a crucial time for Indian Prime Minister Narendra Modi, who wants to solidify New Delhi's business-friendly image ahead of national elections early next year.
The 11th round of talks was concluded recently in London during a visit by Barthwal and Commerce and Industry Minister Piyush Goyal.
Out of the total 26 chapters in the FTA, discussions on 19 have been closed including issues related to the sensitive automobile sector, Barthwal said.
However, the countries have yet to iron out differences on intellectual property rights, rules of origin and an investment treaty, separate trade ministry sources said.
An agreement in principle has been reached on the issue of rules of investment but modalities are still being worked out by customs authorities of both countries, Barthwal said.
"Nothing is final till everything is final," he said when asked about details of concessions India was offering to the UK, adding that the next round of negotiations will be held shortly.
India is pushing for a "zero tariff" for textile, leather and other labour-intensive manufacturing sectors while Britain had sought tariff concessions in other areas, said Barthwal.
Bilateral trade between India and the United Kingdom rose 16.6% year-on-year to $20.42 billion in the 2022/23 fiscal year ending in March.
