May told the House of Commons during Prime Minister's Questions (PMQs) that India was among the countries that had expressed an interest in trade deals with the UK.
"As we leave the EU, we will forge our own trade deals. The leaders from India, Mexico, South Korea and Singapore said they would welcome talks to remove trade barriers. President Xi also made clear that China would welcome discussions about trade with the UK," she said.
In reference to her government's plans on leaving the European Union (EU) in the wake of the June 23 referendum in favour of Brexit, the Prime Minister refused to provide a "running commentary" on her plans.
She said in her statement to Parliament: "On 23rdJune, the British people were asked to vote on whether we should stay in the EU or leave. The majority decided to leave. Our task now is to deliver the will of the British people and negotiate the best possible deal for our country.
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"And I say that because that is not the best way to conduct a strong and mature negotiation that will deliver the best deal for the people of this country," she said.
While giving no more details, she promised a specific British variant on non-membership association with the EU, one that would be "ambitious and bold".
The British premier also used her first parliamentary appearance after a summer break to embarrass Opposition Labour leader Jeremy Corbyn over the impending Labour party leadership election.
"Mr Speaker, what we do know is whoever wins the Labour leadership, we are not going to let them anywhere near power again," she said.