Type IIb supernovae (SNe) present a unique opportunity for understanding the progenitors of stripped-envelope SNe because the stellar progenitor of several SNe IIb have been identified in pre-explosion images. In this paper, we use Bayesian inference and a large grid of non-rotating solar-metallicity single and binary stellar models to derive the associated probability distributions of single and binary progenitors of the SN IIb 2016gkg using existing observational constraints. We find that potential binary star progenitors have smaller pre-SN hydrogen-envelope and helium-core masses than potential single-star progenitors typically by 0.1 M and 2 M , respectively. We find that, a binary companion, if present, is a main-sequence or red-giant star. Apart from this, we do not find strong constraints on the nature of the companion star. We demonstrate that the range of progenitor helium-core mass inferred from observations could help improve constraints on the progenitor. We find that the probability that the progenitor of SN 2016gkg was a binary is 22% when we use constraints only on the progenitor luminosity and effective temperature. Imposing the range of pre-SN progenitor hydrogen-envelope mass and radius inferred from SN light curves, the probability that the progenitor is a binary increases to 44%. However, there is no clear preference for a binary progenitor. This is in contrast to binaries being the currently favored formation channel for SNe IIb. Our analysis demonstrates the importance of statistical inference methods to constrain progenitor channels.