Yes, it is possible. A neutral object can be attracted by both charges. When the object is taken near the rod which is positively charged, a negative charge is induced on the surface of the object. And when it is taken near the rod with the negative charge, positive charges are induced on the surface of the object. This process is called induction.
So, a neutral object can change the net charge on its surface and allow attraction.
Hence the answer is option a.