  Primary very high energy $\gamma$-rays from $\gamma$-ray bursts (GRBs) are
partially absorbed on extragalactic background light (EBL) photons with
subsequent formation of intergalactic electromagnetic cascades. Characteristics
of the observable cascade $\gamma$-ray signal are sensitive to the strength and
structure of the extragalactic magnetic field (EGMF). GRB 190114C was recently
detected with the MAGIC imaging atmospheric Cherenkov telescopes, for the first
time allowing to estimate the observable cascade intensity. We inquire whether
any constraints on the EGMF strength and structure could be obtained from
publicly-available $\gamma$-ray data on GRB 190114C. We present detailed
calculations of the observable cascade signal for various EGMF configurations.
We show that the sensitivity of the Fermi-LAT space $\gamma$-ray telescope is
not sufficient to obtain such constraints on the EGMF parameters. However,
next-generation space $\gamma$-ray observatories such as MAST would be able to
detect pair echoes from GRBs similar to GRB 190114C for the EGMF strength below
10^{-17}--10^{-18} G.
