Structures of planar and bowl-shaped circulenes as well as their stacks with G-quartet (G4) have been investigated through dispersion-corrected Density Functional Theory (DFT-D). The binding energies are substantial $\tilde ∼$10 kcal/mol with d ∼3.5 Å between the stacking rings. The calculations show that G4 binds much more effectively to planar circulenes as compared to bowl shaped molecules. The strength of binding between a G-quartet and a non-planar circulene molecule depends on the orientation of the circulene (concave or convex) with respect to G-quartet. An AIM analysis of the M05-2X wave-functions has also been performed to confirm the presence of weak intermolecular interactions between guanine quartets and circulenes. Apart from 𝜋-stacking interactions, the concave bowl-shaped circulenes also interact with G4 through C-H$\cdots \pi$ interactions. The charge transport properties between the two moieties have also been analysed through effective transport integral. The calculations provide an understanding for the basis of molecular recognition by G4 for non-planar systems.