It all depends on what the intent of your project is. Differential Expression Analysis will tell you if certain genes are notably expressed in some of your samples relative to all samples. If you do correlation between samples, the information you are getting isn't quite the same; with correlation between samples you find out how similar the expression profiles (taking only the genes of your analysis into account) of your samples are (careful since this could be for biological reasons or because of batch effects).

You can certainly present the results in a heatmap, but of course that won't change the fact the there's no significant difference in the results. If there being obvious correlation is sufficient to support the broader argument that you're trying to make then great, otherwise it may not help you much.