I've been assuming that means the literal and most popular translation of ESP: Extra- Sensory Perception. That sort of self-defines ESP as being beyond known physics, and certainly cannot be applied to clues obtained by seeing body language or hearing faint voicings.
It gets a bit ambiguous if we also include senses that have not yet been discovered and which may not exist all. For example: reading the electrical impulses of a brain by the ability of another brain to tune in the faint electromagnetic impulses caused by the first. Even this would violate much of what we think we know about the physics of the strength and propagation of these electromagnetic signals, as well as what we think we know as to the biology: that we only have 5 senses, and that we can't understand how a brain can sense these very weak signals (and to decode them as a thought in the face of the huge number of similar signals coming from the many neurons in the signaling brain). It certainly flies in the face of the results of well-designed tests that have been used to evaluate the ability of brains to detect ESP, or brains to detect even even simple electromagnetic signals.
Again, I hate to use the word impossible (there may be a pink unicorn in my crawl space after all), but I would say that ESP is not compatible with our current understandings of biology/physics, which generally view people as having 5 senses and which do not have a known mechanism by which a thought could be propagated by one brain and received by another. ESP would therefore require a major scientific rethink if it was ever discovered.
When I think of ESP, I think of an ability that we have not seen before and for which no causal mechanism (or physical explanation) currently exists. This could be accurately predicting the future, telepathy, etc. There is no law of nature which states that people can't predict the future. We just haven't observed anyone with the ability. Perhaps the MWI of QM is correct, and they're able to scan other worlds in some way and assign probabilities for this one.