But Mr Sunak has refused to put an “artificial deadline” on when he wants to see a deal signed off.
He is said to think that his predecessors’ habit of setting target dates for ratifying post-Brexit trade terms was damaging to the UK’s negotiating position.
Although we've made enormous progress, there is still hard work to go
Prime Minister Rishi Sunak
Former prime ministers Boris Johnson and Liz Truss both expressed a desire to have a pact with the emerging global powerhouse wrapped up by October 2022 to coincide with the Hindu celebration of Diwali.
Mr Sunak said he and Mr Modi agreed that “there is a good deal to be done”.
Speaking to Asian News International (ANI) on Friday ahead of his bilateral meeting with Mr Modi, he said: “Both Modi and I are keen to see a comprehensive and ambitious trade deal concluded between our two countries.
“Both of us think that there is a good deal to be done. But trade deals always take time. They need to work for both countries.
“And although we’ve made enormous progress, there is still hard work to go.”
The comments appeared more positive than when he told the UK press pack only hours earlier that a free trade agreement with India was “not a given”.
The Conservative Party leader, who is the first British prime minister of Indian descent, said the summit was “not the forum” to hold in-depth discussions about the hurdles holding up a trade agreement.
However, he confirmed he would “touch on” the negotiations with the Hindu nationalist leader on Saturday.
The deal is reportedly being held up by a number of issues, including a disagreement over the number of visas for Indians to work in the UK and differences over the level of access British car manufacturers should be given to India’s market of 1.4 billion people.
A crucial difference between London and New Delhi has been on their stance on Russia’s invasion of Ukraine.
Mr Sunak has been outspoken in condemning Russian president Vladimir Putin’s 19-month assault on Kyiv while India has kept ties open with the Kremlin since Moscow’s forces crossed the Ukrainian border in February 2022.
The Prime Minister suggested he would not be pressing Mr Modi to go further in supporting Ukraine against the Russian invasion.
Before meeting the world leaders of today I’ve been meeting with the world leaders of tomorrow.
It’s been fantastic to visit students and staff here at @inBritish - a reflection of the living bridge that exists between the UK and India. pic.twitter.com/mYc2uZP7kc
— Rishi Sunak (@RishiSunak) September 8, 2023
Asked for his view on the Indian position on the conflict, he told ANI: “Well, it’s not for me to tell India what positions to take on international issues, but I know India rightly cares about the international rule of law, the UN charter and respect for territorial integrity.
“I think those are things that are universal values that we all share. Those are things that I believe, and India, I know, believes in those things too.”
Mr Modi has been placed front-and-centre of the two-day G20 summit being held at Bharat Mandapam, with his face displayed on thousands of posters around the city advertising the gathering.
Indian authorities are looking to use the opportunity to bolster the country’s worldwide reputation, with US president Joe Biden among the leaders flying in.
But a lockdown in place around the summit venue has made it difficult to travel around the Indian capital and press access has been heavily restricted.
On Saturday, Mr Sunak will hold separate meetings with Singapore prime minister Lee Hsien Loong and Mauritian leader Pravind Jugnauth on the fringes of the summit.
In the evening, the Prime Minister and his wife Akshata Murty will join leaders for a dinner hosted by Mr Modi. Ms Murty is the daughter of NR Narayana Murty, the billionaire co-founder of Indian IT giant Infosys.
Ahead of the Singapore bilateral, Downing Street announced a new strategic partnership with the Asian Commonwealth nation.
It involves enhanced shared security between the two, along with efforts to harness the UK and Singapore’s expertise in new technologies like cyber and artificial intelligence to create jobs in both countries, No 10 said.
Mr Sunak said: “This new agreement with Singapore will take us even further in delivering our priorities and ensure that, as we map the future of the world economy, we are doing so alongside our closest partners.”