Graphene has been used as a catalyst to reduce the energy barrier for corannulene inversion. For such a catalytic study, corannulene structures are normally assumed to already be in close proximity to graphene, either in the concave-up or concave-down orientation. Here we use both the Lennard-Jones potential (pair-wise dispersion model) and density functional theory calculations to show that corannulene at a distance further away from graphene can adopt various orientations to optimise its interaction with graphene.