Russian Federation was expelled from what was then known as the Group of Eight in 2014 after it annexed Crimea from Ukraine.
Trump has also invited Australia, South Korea and India.
On Monday, Canadian Prime Minister Justin Trudeau said that Russia's "continued disrespect and flaunting of worldwide rules and norms is why it remains outside of the G7 and why it will continue to remain out".
During the summit, the G7 president normally invites heads of states of one or two countries to attend the meeting as a special invitee.
The spokesman told reporters: "Decisions on G7 membership need to be made unanimously".
"China believes all global organisations and conferences should be conducive to mutual trust between countries to upholding multilateralism, promoting world peace and development", Chinese Foreign Ministry Spokesperson Zhao Lijian said at a press conference. "Russia was removed following its annexation of Crimea and we are yet to see evidence of its behavior that would justify its readmission".
British Prime Minister Boris Johnson's spokesman, James Slack, said the United Kingdom would "look at the detail of what the U.S.is proposing", and also noted that it's customary for the host to invite other leaders as guests. The U.S. did not formally join the deal, but Trump helped to broker it and the country's production has dropped significantly as shale producers shut down wells due to low prices and weak demand.
"At recent G7s, the host country has invited countries from outside the group".
In addition to Russia's 2014 expulsion, The UK has had more recent events tarnish Russia's relationship with the country.
Despite heavy opposition from his counterparts in the G7, Donald Trump has repeatedly suggested the former member should rejoin.
The Kremlin in a press release on Monday said that Trump had informed Putin during a Monday phone call about Washington's plans to hold an expanded G7 summit in September, with the possible invitation of the leaders of Russia, Australia, India and the Republic of Korea. Trump has declared the USA would withdraw from the World Health Organization, citing the group's alleged biased toward China.