The Prime Minister has, according to India’s ministry of external affairs, accepted the invitation following his first return to the country of his heritage since he entered Downing Street.
The prospect of Mr Sunak taking up the offer of an “early” trip back to India raises the possibility that a breakthrough on a UK-India free trade agreement could be approaching.
Both leaders suggested, following their meeting at the G20, that the sticking points in the negotiations could be overcome, with India previously saying a deal could be reached before the end of the year.
A trade pact with India, an agreement that could grant more favourable access for British companies to a market of 1.4 billion people, is seen as a major post-Brexit prize by the Conservative UK Government.
Current hurdles to a deal reportedly include disagreement over an increase of visas for Indians to work in the UK and differences over rules around selling British-made cars to India.
The Prime Minister’s final day in New Delhi on Sunday saw him confront the Chinese premier after the arrest in the UK of a parliamentary researcher on suspicion of spying for Beijing.
During a brief meeting on the fringes of the summit, Mr Sunak said he told Li Qiang that his country’s interference in British democracy was “unacceptable”.
Downing Street had been reluctant ahead of the trip to confirm whether a meeting with Mr Li, who attended the summit in place of president Xi Jinping, was being sought.
Officials briefed that the rendezvous was only confirmed hours before the two politicians spoke.
The face-to-face meeting comes only days after Foreign Secretary James Cleverly became the first UK foreign secretary for five years to visit China, in a trip that was criticised by hawkish Tory MPs.
In an unexpected development at the Indian summit, officials managed to secure consensus for a joint statement, with all 20 of the world’s top economies signing off on wording in relation to the situation in Ukraine.
But Kyiv hit out at the communique after Russia and China objected even to language that they had agreed to last year at the G20 summit in Bali when Moscow’s “aggression” was cited.
Oleg Nikolenko, a spokesman for the Ukrainian foreign ministry, tweeted: “We are grateful to the partners who tried to include strong wording in the text.
“In terms of Russia’s aggression against Ukraine, G20 has nothing to be proud of.”
Mr Sunak defended the joint statement, arguing it included “very strong condemnation” of the impact Russia’s invasion was having on both Ukrainians and the world’s most vulnerable people.
The G20 called for the reimplementation of the Black Sea Grain Initiative, a deal collapsed by the Kremlin in July that allowed safe passage for cargo ships transporting food from Ukraine’s southern ports, and urged for attacks on grain stores to cease.
Speaking to broadcasters at the summit venue shortly before his flight back to London, the Prime Minister said: “The G20 is obviously a large collection of countries that don’t always necessarily share the same values and the same perspective.
“But it is important that the G20 has come together and issued very strong condemnation of the impact of the war in Ukraine on food prices and energy security.
“That is something that I was keen to highlight, I’m glad it is there in the statement in black and white.”
The Tory leader and his wife Akshata Murty visited the Akshardham temple in the Indian capital on Sunday morning ahead of the third and final summit session.
Mr Sunak and Mrs Murty, both practising Hindus, joined in with Sanskrit singing as they made prayer offerings to a golden statue of Lord Swaminarayan.
Afterwards, the couple headed to join other G20 leaders, including US president Joe Biden, at the Raj Ghat memorial in the city to pay tribute to the Indian independence leader Mahatma Gandhi.
The summit proved a tightly controlled affair, with Indian organisers largely keeping the press away from the leaders’ meetings.
Despite that, Mr Sunak and his wife, the daughter of NR Narayana Murty, the billionaire co-founder of Indian IT giant Infosys, proved a huge hit with Indian delegates and locals.
Britain’s first Prime Minister of Indian descent was regularly mobbed by people asking for photos, with security staff having to usher him away from a selfie-demanding crowd in order to make his departure flight.