This depends on how you imagine doing this. If we had full access to the behavior of many neurons or sensibly sized clusters, and we understood enough about how most or all of the components interact, then quite likely we could. But we are also very far from having good spatial and time resolution simultaneously for neuroimaging methods. Again, even if we did, we'd still have to know what it all means in order to infer what is really happening.
With current technologies, such as fMRI or EEG, we can only get coarse measures for certain things. The general mood of a person is probably not difficult to predict with FMRI in some cases, but very specific things, like exact words or images going through your mind, are much more difficult.
In short, there is no theoretical reason why we wouldn't be able to eventually, but we'll need better tools and cognitive models.