The problem for Snowden is that these countries wouldn’t gain anything by giving him asylum. He has presumably already revealed everything he knows or is planning to soon. Foreign governments can benefit from these disclosures without doing anything for Snowden in return. Most spies sell their secrets to other countries rather than give them away, and bargain hard for an escape route.
Meanwhile, Snowden is not the type of person you want living in your country. Countries don’t grant citizenship or permanent residence to people they know to be felons. These people are more trouble than they’re worth. For all his IT skills, Snowden is not likely to be an appealing employee to a government or business that might otherwise be able to use them.
Snowden has few options left. Any country with an extradition treaty with the United States would probably extradite him—so his efforts to get into Germany or France are pretty pointless. Perhaps, if he reached Cuba or Bolivia, he could stay in one of those countries, in the process giving up the civil liberties that he holds so dear.