Russia and the US are backing opposite sides in the conflict, but officials say the statement could soon be agreed.
This could include the proposed peace conference in Geneva, and more access for deliveries of humanitarian aid.
The summit, which is now in its final day, is also discussing tax evasion and efforts to boost trade.
Russian Deputy Foreign Minister Sergei Ryabkov said Moscow would sign up to the statement on Syria later on Tuesday.
But he stressed the Kremlin wanted each of the Syrian sides in the talks to select not only their own delegations but the future terms of any transitional government.
Sergei Ryabkov sidestepped the question of whether this could leave open a role for President Bashar al-Assad in the future.
To try to get as much consensus as possible on Syria, UK Prime Minister David Cameron – who is hosting the summit – held a working dinner on Monday night.
The leaders were alone, with no officials present, allowing them to express their views frankly.
After the meeting, British officials appeared more optimistic that an agreement could be reached on the joint statement on Syria.
However, they said it would take more work to agree the precise language.
Earlier on Monday, the British had raised the possibility of the other G8 nations issuing an end-of-conference statement without the participation of Russia.
But it now seems that Vladimir Putin is willing to consider some kind of joint stance, according to officials.
The communiqué is likely to back the launch of Syrian peace negotiations in Geneva, and insist that humanitarian aid agencies like the Red Cross are given access to all parts of the country.
Any statement which emerges may not be all that ambitious, correspondents warn – and even then, it is far from certain that any agreement will change the appalling reality in Syria itself.
The White House announced last week that it would provide military aid to the Syrian rebels. Russia meanwhile supplies weapons to the government of President Bashar al-Assad.
Presidents Barack Obama and Vladimir Putin met for an hour of bilateral talks on Monday, and at a sombre press conference afterwards it was clear they had had a difficult exchange.
Both presidents acknowledged their differences but said they shared a common desire to stop the bloodshed.
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