Can an asteroid have a magnetic field? Some M-type asteroids are believed to be metallic, even possessing Nickel-Iron.
Given 


*

*the proximity of the asteroid belt to Jupiter's magnetosphere, 

*the regularity of motion of any given M asteroid relative to Jupiter

*the ease with which Nickel/Iron may be magnetized, and 

*the strength of Jupiter's magnetic field


Is it reasonable to expect an M-type asteroid that fulfills such conditions to exhibit a magnetic field?
 A: In a general sense, yes, asteroids can have magnetic fields - for example, in the article "Magnetic Field Signatures Near Galileo's closest approach to Gaspra" (Kivelson et al. 1993), Gaspra, an S-type asteroid with an unusually metal and olivine abundance exhibited what has been suggested by the article as a measurable magnetic field.
In the article "Observations of the Magnetic Fields Inside and Outside the
Solar System: From Meteorites (~ 10 attoparsecs),
Asteroids, Planets, Stars, Pulsars, Masers, To Protostellar
Cloudlets (< 1 parsec)" (Vallee, 1998) (section 2.1.3 on page 6-7), further information is provided about the asteroid Gaspra and also mentions another S-type asteroid 243 Ida as having a measurable (likely to be remanent) magnetic field.
According to the article "Possible evidence for partial differentiation of asteroid Lutetia from Rosetta" (Weiss et al. 2012), the M-type asteroid 21 Lutetia also had a measurable magnetic field.  However, 

whether Lutetia has substantial fine-scale remanent
  magnetization like that expected from an internal core
  dynamo (Weiss et al., 2008) or externally generated fields in the
  early solar system (Weiss et al., 2010).

Additional resources:

Weiss, B.P., Berdahl, S., Elkins-Tanton, L.T., Stanley, S., Lima, E.A., Carporzen, L.,
  2008. Magnetism on the angrite parent body and the early differentiation of
  planetesimals. Science 322, 713–716.
Weiss, B.P., Gattacceca, J., Stanley, S., Rochette, P., Christensen, U.R., 2010.
  Paleomagnetic records of meteorites and early planetesimal differentiation.
  Space Science Reviews 152, 341–390.

