  The large-number hypothesis conjectures that fundamental constants may vary.
Accordingly, the spacetime variation of fundamental constants has been an
active subject of research for decades. Recently, using data obtained with
large telescopes a phenomenological model in which the fine structure constant
might vary spatially has been proposed. We test whether this hypothetical
spatial variation of {\alpha}, which follows a dipole law, is compatible with
the data of distant thermonuclear supernovae. Unlike previous works, in our
calculations we consider not only the variation of the luminosity distance when
a varying {\alpha} is adopted, but we also take into account the variation of
the peak luminosity of Type Ia supernovae resulting from a variation of
{\alpha}. This is done using an empirical relation for the peak bolometric
magnitude of thermonuclear supernovae that correctly reproduces the results of
detailed numerical simulations. We find that there is no significant difference
between the several phenomenological models studied here and the standard one,
in which {\alpha} does not vary spatially. We conclude that the present set of
data of Type Ia supernovae is not able to distinguish the standard model from
the dipole models, and thus cannot be used to discard nor to confirm the
proposed spatial variation of {\alpha}.
