Including the Russian president would significantly ease international pressure on Putin, who has been isolated by most of the West as a result of the invasion of Ukraine.
"If he came, it would probably be a big help," US President Donald Trump says.
The United States is hosting the G20 this year and Trump has promised a grand summit in December in Florida.
Trump says he doubts Putin will choose to participate, but at the same time criticizes the decision to exclude Russia from the G8 over the country's invasion of Crimea in 2014.
"President Putin was very offended by that - and rightly so," says Trump.
