I am in no way a physicist but I do have a fascination with physics. My question is if magnets are being explored / studied as a potential source to achieve the speed of light and if that is even physically possible?
It is not physically possible to accelerate any object with mass to the speed of light using magnets. There are a few reasons for this.
First, it is a widely held belief that it is impossible for anything with mass to achieve light speed period; that it would take an infinite amount of energy to accomplish this and there is slightly less energy than that in all of existence.
Second, since magnets operate on the principles of the electromagnetic force, and since a photon (i.e. light) is an embodiment of the electromagnetic force in the form of fluctuating electric and magnetic fields, then using a magnet to accelerate something means that on a very basic level, you are using massless photons to impart momentum on the object. Furthermore, since light is limited to light speed and since they have no mass, they can never impart enough momentum on something with mass to achieve the same speed as them. That means that one cannot achieve light speed using any means that, at its most basic level, utilizes the electromagnetic force (rockets, solar sails, a good hard push, and magnets are all included).
Having said all of this, you may be interested to know that we currently do use magnets to accelerate things to very nearly the speed of light. In particle accelerators, an advanced array of magnets are aligned and used such that they can accelerate a proton (or other particle) to extremely close to the speed of light.