The call, which officials said had been scheduled for several days, will come after Snowden said he wanted to claim temporary asylum in Russia.
Top US officials meanwhile warned Moscow that offering such status to Snowden would undercut its statements that it did want the affair to harm relations with Washington.
"Providing a propaganda platform for Mr Snowden runs counter to the Russian government's previous declarations of Russia's neutrality," Carney said.
"It's also incompatible with Russian assurances that they do not want Mr Snowden to further damage US interests."
Carney also renewed a US call on Russia to expel Snowden so that he could be returned to American soil to face trial for leaking US national security secrets.
Carney said that Obama's conversation with Putin would address Snowden, along with other key issues ahead of Obama's planned trip to Russia in September.
Snowden earlier told activists he wanted to claim asylum in Russia until he can travel on to Latin America, in his first encounter with the outside world since becoming marooned at a Moscow airport three weeks ago.