David Cameron is considering taking thousands of unaccompanied Syrian refugee children from migrant camps in Europe.
The Prime Minister will decide in the "coming days and weeks" how children who have fled to Europe but been separated from parents can be helped, the International Development Secretary told Sky News.
If Mr Cameron agrees to take refugee children from Europe it would represent a softening of the Government position.
Britain has already agreed to take 20,000 Syrian refugees but had insisted it would only take them from the refugee camps in the Syrian region - and not draw from the camps in Europe.
However, pressure from charities and the intensification of the migrant crisis in Europe has prompted a rethink and the Government is considering taking some children from Europe as part of the 20,000.
According to charity estimates, there are as many as 3,000 lone refugee children in Europe.
International Development Secretary Justine Greening told Dermot Murnaghan: "We've steadily evolved our approach as this crisis has evolved, we've been right at the forefront, frankly, of helping children who have been affected by this crisis and will continue to look at how we can do that over the coming days and weeks."
Labour's shadow home secretary Andy Burnham said: "David Cameron has been found guilty of a real lack of judgement and leadership during this refugee crisis.
"He has been pursuing his own individual demands on EU migration while the rest of Europe has been grappling with the biggest humanitarian crisis since the Second World War. He has left Britain looking blinkered and selfish.
"Just miles from our own doorstep, there are hundreds of refugee children in makeshift French camps living alone in abhorrent conditions.
"Britain can, and should, be doing more to give those kids a place of safety and I believe the vast majority of people here would support it."
Liberal Democrat leader Tim Farron told Sky News it would be pretty "mean-spirited" if the Government included the number of unaccompanied children in the 20,000 figure.
His comments come after Jeremy Corbyn called on the Government to let 3,000 migrants in the French camps come to Britain - especially unaccompanied children. The Labour leader also accused the Government of not doing enough to help.
Europe continues to struggle to deal with the migrant crisis. EU officials are preparing to meet to discuss suspending Europe's border-free travel zone, drawn up under the Schengen agreement, for two years.
On Friday, the French prime minister, Manuel Valls, warned that the refugee crisis put the future of the European Union, whose key principle is the freedom of movement of people between countries, in "grave danger".
