  In the magneto-centrifugal mechanism for jet formation, accreting neutron
stars are assumed to produce relativistic jets only if their surface magnetic
field is weak enough ($B \sim 10^8$ G). However, the most common manifestation
of neutron stars are pulsars, whose magnetic field distribution peaks at $B
\sim 10^{12}$ G. If the neutron star magnetic field has at least this strength
at birth, it must decay considerably before jets can be launched in binary
systems. We study the magnetic field evolution of a neutron star that accretes
matter from the wind of a high-mass stellar companion so that we can constrain
the accretion rate and the impurities in the crust, which are necessary
conditions for jet formation. We solved the induction equation for the
diffusion and convection of the neutron star magnetic field confined to the
crust, assuming spherical accretion in a simpliflied one-dimensional treatment.
We incorporated state-of-the-art microphysics, including consistent thermal
evolution profiles, and assumed two different neutron star cooling scenarios
based on the superfluidity conditions at the core. We find that in this
scenario, magnetic field decay at long timescales is governed mainly by the
accretion rate, while the impurity content and thermal evolution of the neutron
star play a secondary role. For accretion rates $\dot{M}\gtrsim10^{-10}$
M$_{\odot}$ yr$^{-1}$, surface magnetic fields can decay up to four orders of
magnitude in $\sim$10$^7$ yr, which is the timescale imposed by the evolution
of the high-mass stellar companion in these systems. Based on these results, we
discuss the possibility of transient jet-launching in strong wind-accreting
high-mass binary systems like supergiant fast X-ray transients.
