Answering your biological question, there are some chance of some genes being regulated by the same transcription factors set to be co-expressed, some times this pattern it's very sharp in particular when you expect a non-return control point (like development or cell-specificity). In general this pattern is really noisy, several genes controlled by the same TF barely conserve a co-expression because you know, there are other levels of regulation (transcription rate, mRNA stability, protein modifications, ...). Therefore a lot of strong statistical tests are required and bench validation.

I think FIRE is a potentially useful tool because it provides motif and GO enrichment (although it is specifically centered around motifs) for discrete groups:

https://tavazoielab.c2b2.columbia.edu/FIRE/

So, if you define your co-expressed genes as clusters (or using something like k-means clustering), this is meant to address your type of question. I believe it provides both upstream and downstream motifs. There are other similar tools, but this is what I can think of off the top of my head.