Britain has called for Syrian President Bashar Assad's ouster and has said the current EU arms embargo may need to be lifted to help opposition forces. Russia, a key ally of Syria, opposes further action against Damascus, although it recently agreed with the United States to convene an international conference to find a political solution to the conflict.
Britain has recognized the coalition of forces opposed to the Syrian government and increased its support, providing armored vehicles and body armor, as well as communications and medical supplies.
The BBC reported British and Russian leaders hope to find common ground on Syria before next month's meeting of the Group of Eight in Northern Ireland.
The United Nations estimates 70,000 people have died since Syria's civil war began in March 2011.
A British Foreign Office spokesman told the BBC that leaders haven't decided whether to seek to end the EU arms embargo when the matter is considered at the end of the month.
A senior official told The Daily Telegraph the timing of Cameron's visits with Putin in Sochi this week and with U.S. President Barack Obama next week was "coincidental [but] very useful."
"We are interested in trying to put together a Syria conference in London," the official said.