"We have to carefully analyse, watch what's going on, and see at what stage and how we can participate in this process and use it, including by the way, to avoid any restrictions in the sphere of global financial activity", Putin said.
Russian Federation was expelled from the group in 2014 after it invaded and annexed Crimea and for its support of pro-Russia separatists in Ukraine.
Responding to Trump's call for Russia's return to G8, the Kremlin said that Moscow is focused on other negotiating formats.
He referred to a meeting of President Donald Trump and North Korean leader Kim Jong Un in Singapore on Tuesday, saying "we positively view the intentions of Pyongyang, Seoul and Washington to reach a comprehensive settlement of the crisis through talks".
Speaking at a joint press point with Chinese Foreign Minister Wang Yi in Brussels on June 1, the European Union's foreign policy chief Federica Mogherini said the bloc and China share commitment to preserve the nuclear agreement and to work for its continuation. Founded in 2001, it was originally conceived as a vehicle for resolving border issues, fighting terrorism and - more implicitly - to counter American influence in Central Asia after its invasion of Afghanistan.
They have met in person twice - once at a formal bilateral meeting in Germany and once on the sidelines of a leaders' summit in Vietnam.
Russian President Vladimir Putin said Sunday he was ready for a face-to-face meeting with US President Donald Trump over the dangers of a new arms race. "However, we will be glad to see everyone in Moscow", Putin said to reporters.
Putin says some nations including Austria have offered to host his summit with Trump.
The meeting with China's president Xi Jinping took place on Sunday on the sidelines of the Shanghai Cooperation Organization summit in the eastern coastal city of Qingdao, and comes at a time when Iran faces reimposition of sanctions by the United States, which could impact its crude oil exports.
Putin's remarks follow a report that White House officials were working toward setting up a meeting.
The United States and Russia's relationship has remained a big part of Trump's presidency since the 2016 election.
The Russian president visited China between Friday and Sunday.
US President Donald Trump last month announced that the US was withdrawing from the Iran nuclear deal signed by the Obama administration in 2015 under which Tehran had agreed to limit its nuclear activities and allow in worldwide inspectors in return for the lifting of crippling economic sanctions. Washington has frowned upon India's decision to go ahead with the acquisition of the Russian Triumf S-400 missile system at a cost of Rs. 40,000 crore and has hinted that future Indo-US defence relations may be adversely affected if New Delhi does not resile from its stand. India, apparently, is in no mood to do so and the necessary agreement may be signed by New Delhi and Moscow this October.
Xi said the deal is "conducive to safeguarding peace and stability in the Middle East and the worldwide non-proliferation regime, and should continue to be implemented earnestly", according to Xinhua.