Any such meeting would see the presidents address "several questions", Lavrov said, without elaborating other than to add that "above all, we must normalise dialogue" with Washington.
"We assume that a meeting will take place, given that the two presidents will be in the same town at the same time, same building, even the same room," Lavrov said at a press conference with German Foreign Minister Sigmar Gabriel.
"It wouldn't be normal if they didn't talk," the top Russian diplomat added.
Gabriel welcomed the possibility that the summit could bring Trump and Putin, who have yet to meet, together.
Also Read
During last year's US presidential campaign, Trump often suggested he wanted improved ties with Russia.
At the end of March, Putin said he was ready to meet with Trump at the G20 summit, but neither Moscow nor Washington has confirmed any such plan.
"Above all, it is necessary to normalise dialogue, so that dialogue is based on the vital interests of Russia and the United States," said Lavrov, stressing that there are always meetings "on the margins" of a G20 summit.
On Monday The White House warned of possible reprisals against the Russian-backed Syrian regime, in response to intelligence suggesting President Bashar al-Assad may be preparing a chemical weapons attack.
The following day, Kremlin spokesman Dmitry Peskov denounced the US "threats" against the Syrian regime which he called "unacceptable".
If the US carries out its threat Russia will "react, in proportion to the situation," Lavrov said today.
Meanwhile Pentagon chief Jim Mattis accused Putin of making international "mischief".
Speaking to students in Germany to commemorate the 70th anniversary of the Marshall Plan to rebuild World War II- ravaged Europe, Mattis said Russia had chosen to challenge the "secure and peaceful" post-war order.
US intelligence suspects that Putin orchestrated a sweeping presidential election campaign to tilt the vote in Trump's favour.
But Trump declared himself the victim of the "greatest witch hunt" in American political history, refuting accusations that he tried to quash a probe into collusion between his campaign team and Russia.
Disclaimer: No Business Standard Journalist was involved in creation of this content