Can the inverse of a micelle be formed with non-polar solvents? A micelle is formed due to the clustering of soap molecules wherein the interior of the cluster is formed by the hydrophobic end and the ionic ends are on the surface of the cluster. 

So, if a non-polar solvent is used (Assuming non-polar solvents dissolve non-polar solvents), can the reverse of micelle be formed? That is, wherein the ionic end forms the interior and the hydrocarbon end the exterior?
Yes, they are aptly enough called inverse micelles, eg such as formed by the detergent AOT. While you retain the hydrophobic/philic balance typical of a water-soluble detergent, wherein you have a long hydrophobic tail and hydrophilic headgroup, you generally have to alter the headgroup area (making it smaller relative to the tails) to favor inverted phases of this type. In addition if charged the headgroups will strongly repel, requiring a cosolvent or some counterions to reduce such interactions.