Mr Cameron infuriated supporters of the dissident academic when he failed to mention him by name when raising human rights in talks with Premier Wen Jiabao earlier today.
Downing Street officials refused to confirm whether he planned to do so later in his two-day visit.
But it was thought likely he would take the opportunity of a banquet hosted by Mr Wen this evening or private talks tomorrow with President Hu Jintao to express his concern.
Mr Cameron is the first Western leader to visit China since Mr Liu was awarded the Nobel prize on October 8 and has come under increasing pressure to raise his case with the Chinese leadership during a trip which he had intended to focus predominantly on trade.
Mr Liu was jailed for 11 years last December for subversion after launching a petition for democratic reforms. His case was forced up the agenda when Chinese security agents prevented his lawyer boarding a plane for London at Beijing airport this morning.
Mr Cameron insisted that he would not fight shy of human rights issues in talks with Mr Wen and President Hu.
But he said there would be no "lecturing or hectoring" of his Chinese hosts and he would approach the subject "with respect and mutual understanding, acknowledging our different histories".
It was regarded as a positive and significant development that the Chinese Premier responded to Mr Cameron's mention of human rights by saying that he welcomed dialogue with the UK on this and other subjects.
Aides sought to draw a veil over comments made last year by Education Secretary Michael Gove, who is travelling with the Prime Minister, when he said that China remains "a police state, with thousands executed by government fiat every year". Mr Gove was in opposition when he made the remarks on the 20th anniversary of the Tiananmen Square massacre, they pointed out.
Mr Cameron played down suggestions that support for Mr Liu could jeopardise trade deals, insisting that Britain's relations with China were strong enough to withstand disagreement over political systems.
"Yes, we want a stronger economic business relationship with China - we are the fifth largest economy in the world but we only have 2% of China's imports," he said.
"But our dialogue is mature enough that we cover all of these areas, including human rights."
Today's talks at the Great Hall of the People, near Tiananmen Square, focused mainly on business issues, with both sides agreeing that efforts should be made to boost bilateral trade, which stood at £32 billion in 2009. However, there was no specific Chinese commitment to sign up to Mr Cameron's declared ambition to hit 100 billion US dollars (£62 billion) by 2015.
Mr Cameron has said he hopes Britain's share of this trade will be 30 billion dollars (£19bn)- up from 12.4 billion (£7.7bn) in 2009.
While this will effectively increase Britain's trade deficit with the emerging Far Eastern power, aides said that it will provide a major boost to the UK economy as it emerges from recession.
The meeting concluded with the signing of a £750 million Rolls-Royce agreement to supply and service engines for China Eastern Airlines, which took the total value of deals struck during the visit past the £1 billion mark.
Writing in the Wall Street Journal, Mr Cameron said the visit would provide "a further step forward in UK-China relations, adding momentum to our commercial relationship and cementing an economic and political partnership".
Meeting Mr Wen, he stressed the continuity of his Government's policy towards China with that of its Labour predecessor, in supporting a partnership for growth through free trade.
As well as supplying the luxury goods and creative talent sought by the Far Eastern giant's emerging middle class, the UK can offer a gateway to open up the European Union to Chinese businesses, he said.
Mr Wen welcomed Mr Cameron's characterisation of China's phenomenal economic growth as an opportunity for the West, rather than a threat. And he noted that previous breakthroughs - including the 1973 establishment of full diplomatic relations and Margaret Thatcher's agreement on the return of Hong Kong - had taken place under Conservative prime ministers.
Mr Wen also indicated that China stood ready to co-operate in taking forward the issue of illegal migrants to the UK and the return of around 360 Chinese prisoners in British jails.
In face-to-face talks, the two men also discussed the need to prevent nuclear proliferation in Iran and North Korea and the opportunities for enhanced co-operation in Africa. Mr Cameron raised the issue of Burma, following this week's disputed elections.
The Prime Minister this morning visited a branch of Tesco in Beijing, as well as attending a 600-year-old temple where the British Council are holding courses for social entrepreneurs seeking to provide services like healthcare and education outside the state apparatus.
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