  We perform in this work an analysis of the background dynamics for
$\alpha$-attractor models in the context of loop quantum cosmology. Particular
attention is given to the determination of the duration of the inflationary
phase that is preceded by the quantum bounce in these models. From an analysis
of the general predictions for these models, it is shown that we can be able to
put constraints in the parameter $\alpha$ of the potentials and also on the
quantum model itself, especially the Barbero-Immirzi parameter. In particular,
the constraints on the tensor-to-scalar ratio and spectral tilt of the
cosmological perturbations limit the $\alpha$ parameter of the potentials to
values such that $\alpha_{n=0} \lesssim 10$, $\alpha_{n=1} \lesssim 17$ and
$\alpha_{n=2} \lesssim 67$, for the $\alpha$ attractors T, E, and $n=2$ models,
respectively. Using the constraints on the minimal amount of e-folds of
expansion from the quantum bounce up to the end of inflation leads to the upper
bounds for the Barbero-Immirzi parameter for the $\alpha$-attractor models
studied in this work: $\gamma_{n=0} \lesssim 51.2$, $\gamma_{n=1}\lesssim 63.4$
and $\gamma_{n=2} \lesssim 64.2$, which are obtained when fixing the parameter
$\alpha$ in the potential at the values saturating the upper bounds given above
for each model.
