"We invite Edward to Petersburg and will be happy if he decides to join the dream team of VKontakte programmers," wrote 28-year-old Durov.
Durov's young age and sometimes extravagant statements have earned him comparisons with Facebook founder Mark Zuckerberg.
"No other Internet company in Europe is more popular than VK," Durov said, referring to the shortened name of the social network, which boasts 210 million registered users and is based in Saint Petersburg.
"I think Edward would be interested in working on security of personal data of the millions of our users."
A former contractor for the NSA, Snowden has been in Russia since June 23, when he arrived from Hong Kong after leaking details of US surveillance operations in the world.
He had stayed in the airport transit zone until Thursday, when Russia granted him asylum status for one year, allowing him to formally cross the border.