I have never read that it makes sense to talk about any variable in a model which is not significant.

Possibly I'm interpreting "talk about" in a different way than you mean, but I'm sure one might sometimes want to say things about an effect that isn't significant? People say all kinds of things about all kind of topics :yup:

For one of my multiple regressions, the overall regression model is non-significant (.17) with a very small adjusted R square of .03. Whilst most of my predictors are non-significant, I have one significant predictor (an interaction). When I asked my supervisor whether such a predictor is worth looking into (i.e plotting a graph to understand the interaction) he seemed to think not, and suggested just briefly mentioning the interaction.

I'd say that the non-significant overall model and low R squared may be useful pieces of information to provide, but they imply pretty much nothing about what you should choose to actually write

*about *in your report. Your study presumably set out to answer some questions: Give the necessary information to answer those questions. If you predicted that a particular effect would be statistically significant, and it isn't, say that. If you predicted that this interaction would be significant and it is, say so.

However, if you

did not specify any hypotheses about this interaction, and don't have any pre-existing reasons to expect it to be important, then

**don't** make a big deal about this interaction or start trying to put together an explanations for why it might be there. Chances are that the interaction may just be noise.