Cameron, who is in India on a short visit during which he met Prime Minister Manmohan Singh at his Race Course residence here, said it will be "good" to meet Modi and that he will do so in time while his government goes ahead with steps to engage with him and his government.
Seeking broadening of bilateral ties, Cameron also said UK and India should be "partners of choice" as both the countries can effectively deal with various challenges like combating terrorism by working closely with each other.
"We have started a proper engagement with Gujarat already and with the First (Chief) Minister there. Our Foreign Office Minister has met with him... The connection is there, the engagement is there. I think the engagement should continue," he said at an interaction with Indian businessmen here.
Asked if he would like to meet Modi in the near future, Cameron said, "In time, yes. It's good to meet. We have an approach of meeting all politicians and leaders. In the end, it will be for the people of India whom to elect. But I'm open to meeting elected leaders."
Although many western nations including Britain and the US distanced themselves from Modi in the immediate aftermath of the post-Godhra 2002 riots in Gujarat, there has been a shift in their position in the last one year.
In March this year, Britain's Foreign Office Minister Hugo Swire met Modi in Gujarat, saying it was "a logical next step" in its relations with the Indian state.
The British Premier later left for Kolkata for a scheduled meeting with West Bengal Chief Minister Mamata Banerjee. It is his first vist to the eastern metropolis.
"This is, I said, a short visit, so this is a government to government visit to India where my first priority is to come and see your Prime Minister. Kolkata is a city I've never been to before... I'm looking forward to the visit," he said.
Cameron, who is visiting India for the third time in as many as years, favoured more meetings and informal discussions with the Indian Prime Minister and said there is a lot in common between India and Britain and the two were good trade partners as well.
"We are one of the oldest democracies... We both have challenges to fight terrorism and we both want to be successes in this global economic race that we are engaged in. We have ties of the past - the history, the language and the culture. But it is the future that excites me, on what Britain and India can do together," he said.
Cameron discussed matters of bilateral interest relations and other issues with his Indian counterpart.
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