E.g. the US tells Norway they should say "yeah sure we won't arrest and extradite you," then go back on their word and arrest him as soon as he enters the country. The US makes some under-the-table bribes or threats to be sure Norway goes along with this scheme.
Something along the lines of "It sure would be a shame if we tanked your economy by making it illegal for US businesses to operate in Norway...those juicy Internet taps Snowden claims we have, well we can't confirm or deny them, but we might or might not know certain delicate things that were said in private by Norwegian politicians, and we might or might not know about certain financial relationships between certain wealthy Norweigans and high-ranking politicians, and it sure would be a shame if the things we might or might not know became public and had unfortunate consequences for your party's political position...now let's talk about how you're going to handle this Snowden situation..."
Also as other posters have pointed out, the US could simply send a CIA team to kidnap or murder him. Norwegian counterintelligence is presumably a lot weaker than Russia's, and their politicians presumably a lot more afraid of the US, so it's probably a lot less risky for the US to run an op like that in Norway than in Russia.