We report a serendipitous extreme ultraviolet observation by EUVE of the fi
eld containing GRB 921013b, similar to 11 hours after its occurrence. This
burst was detected on 1992 October 13 by the WATCH and PHEBUS on Granat, an
d by the GRB experiment on Ulysses. The lack of any transient (or quiescent
) EUV source imposes a 2 sigma upper limit of 1.3 x 10(-12) erg s(-1) cm(-2
) in the 58-174 Angstrom bandpass. In the likely case that GRB 921013b was
extragalactic, and assuming the existence of an X-ray afterglow similar to
those observed for GRB 970228 and GRB 970828, the resulting EUV flux 11 hou
rs after the burst is 1.8 x10(-16) erg s(-1) cm(-2) after correction for ab
sorption by the Galactic interstellar medium. Even if we exclude an intrins
ic absorption, this is well below the detection limit of the EUVE measureme
nt. Although it is widely accepted that gamma-ray bursts are at cosmologica
l distances, if the source of GRB 921013b would be a galactic neutron star,
the data presented here place a lower limit to its distance of similar to
30 pc.