I don't think you can because "current" is a threaded object. It contains 3 things: request, response, session. You could probably serialize much of the data contained in those three objects, however, this will be difficult because they contain functions. Web2py does a lot of this when it generates an error ticket. So maybe you could look into how those tickets are generated.
Also, I have to ask: Why would you want to do this? Web2py does it to provide debugging information when something bad happens and that's about the only reason this type of thing should be done. If there is something else you are trying to accomplish, maybe we can find a better way.
