  The $N^*(1535)$ can be dynamically generated in the chiral unitary approach
with the coupled channels, $K^0 \Sigma^+, K^+ \Sigma^0, K^+ \Lambda$ and $\eta
p$. In this work we evaluate the correlation functions for every channel and
face the inverse problem. Assuming the correlation functions to correspond to
real measurements, we conduct a fit to the data within a general framework in
order to extract the information contained in these correlation functions. The
bootstrap method is used to determine the uncertainties of the different
observables, and we find that, assuming errors of the same order than in
present measurements of correlation functions, one can determine the scattering
length and effective range of all channels with a very good accuracy. Most
remarkable is the fact that the method predicts the existence of a bound state
of isospin $\frac{1}{2}$ nature around the mass of the $N^*(1535)$ with an
accuracy of $6\; \rm MeV$. These results should encourage the actual
measurement of these correlation functions (only the $K^+ \Lambda$ one is
measured so far), which can shed valuable light on the relationship of the $
N^*(1535)$ state to these coupled channels, a subject of continuous debate.
