  Existence of a minimal measurable length, as an effective cutoff in the
ultraviolet regime, is a common feature of all approaches to the quantum
gravity proposal. It is widely believed that this length scale will be of the
order of the Planck length $\lambda=\lambda_0\,l_{_{\rm Pl}}$, where
$\lambda_0\sim{\mathcal O}(1)$ is a dimensionless parameter that should be
fixed only by the experiments. This issue can be taken into account through the
deformed momentum spaces with compact topologies. In this paper, we consider
minimum length effects on the physical quantities related to three parameters
of the $SU(2)$ Nambu-Jona-Lasinio effective model of QCD by means of the
deformed measure which is defined on compact momentum space with ${\mathbf
S}^3$ topology. This measure is suggested by the doubly special relativity
theories, Snyder deformed spaces, and the deformed algebra that is obtained in
the light of the stability theory of Lie algebras. Using the current
experimental data of the particle physics collaboration, we constraint quantum
gravity parameter $\lambda_0$ and we compare our results with bounds that are
arisen from the other experimental setups.
