MPI models implemented in Monte Carlo generators typically rely on the minijet cross section formula derived from the LO collinear factorization supplemented with a $p_T$ cutoff, which slowly grows with the energy. The natural question is whether such a cutoff can be explained (or dynamically generated) from an approach which goes beyond the leading power. One of approaches venturing beyond the leading twist is the High Energy Factorization (HEF) which involves unintegrated gluon distributions and off-shell matrix elements. We have asked two questions: i) whether the minijet formula based on HEF can directly produce the required $p_T$ cutoff by a nonzero transverse momenta of incoming gluons, and ii) whether the inclusive dijet cross section based on HEF contains hints about minijet suppression away from the small $p_T$ region. For the study ii) we constructed a distribution in the relative momentum disbalance of the dijets (relative to the average $p_T$ of jets) which can be characterized by the bimodality coefficient. We checked using Pythia that its energy dependence reflects the $p_T$ cutoff. Thus, we were able to indirectly study a minijet suppression in HEF due to various unintegrated gluon distributions.