  We discuss hadroproduction of 4-jet final state at the LHC within the
double-parton scattering (DPS) mechanism in the context of
large-rapidity-distance jets. For planned and/or being currently performed high
energy experiments this is the kinematical region where searches for BFKL
signal are of the main interest. The DPS contributions are calculated in the LO
collinear approach within the so-called factorized Ansatz. We show that the
relative contribution of DPS is growing with respect to standard single-parton
scattering (SPS) production of dijets and to the BFKL Mueller-Navelet (MN) jet
mechanism at large rapidity distance between jets. This is consistent with
recent studies of DPS effects in the case of double $D$ and double $J/\!\psi$
meson production. The calculated differential cross sections as a function of
rapidity distance between the jets that are the most distant in rapidity are
compared with recent results of LL and NLL BFKL calculations for the
Mueller-Navelet jet production at $\sqrt{s} = 7$ TeV. The DPS contribution is
carefully studied for $\sqrt{s}$ = 7 TeV and $\sqrt{s}$ = 14 TeV and in
different ranges of jet transverse momenta.
