The rethinking -- reversing an announcement Obama made last month when the two leaders met in Northern Ireland -- would also reflect growing strains over the war in Syria, disputes over nuclear weapons, including in Iran, and White House concerns about the Kremlin's treatment of dissidents, administration officials told several news organizations.
The White House, which did not officially comment on the possible meeting cancellation, said it was "deeply disappointed and concerned" by the Thursday conviction of Russian opposition leader Aleksei Navalny, who exposed high-level Kremlin corruption.
He was convicted on embezzlement charges and sentenced to five years in prison.
The White House said the conviction reflected a trend of "suppressing dissent and civil society in Russia."
Putin has said Washington is being hypocritical in complaining about Russian actions when it seeks to prosecute Snowden, who exposed top-secret U.S. surveillance programs. Snowden faces up to 30 years in prison.
The fugitive former contractor, who has been in the transit zone of Moscow's Sheremetyevo International Airport for weeks, formally requested temporary asylum in Russia Tuesday.
But Putin has also said he doesn't want the Snowden matter to hurt U.S.-Russian ties.
"Bilateral relations, in my opinion, are far more important than squabbles about the activities of the secret services," he told Russian reporters who asked Wednesday about the scheduled Moscow meeting.
The meeting would be an extra stop for Obama on a trip to St. Petersburg for the annual Group of 20 nations summit Sept. 5-6.
White House spokesman Jay Carney this week declined several time to say if Obama still planned to go to Moscow.
"The president intends to travel to Russia for the G20 summit," he told reporters Wednesday. "I don't have anything to add to what we've said in the past about that trip."
When pressed, Carney acknowledged to laughter he "might have been deliberately vague, so I'm not sure I can clarify."
But Carney mentioned nothing about a possible cancellation and didn't answer directly when asked if there would be any consequences for Russia if Snowden is not returned.
"We are working with them through normal channels and having conversations with Russian government officials at all levels about this matter," he said. "I am not going to get ahead of that process."
A cancellation would not be the first between Obama and Putin.
In May of last year, when Obama hosted the Group of Eight summit at Camp David, Md., Putin stayed in Russia, citing domestic obligations.