We study the partial swapping of the Fano resonance in a correlated double-quantumdot (DQD) system connected to normal leads by employing the Keldysh non-equilibrium Green function technique in a Coulomb blockade regime. Two types of asymmetries have been considered which occurs when the DQD system undergoes transition from symmetric parallel to i) series and ii) T-shape geometries. It is found that both types of asymmetries exhibit swapping on varying the interdot Coulomb interaction (U12), however, mostly in the first one or first two pairs (out of four pairs) of Fano and Breit-Wigner peaks. Further, for particular values of U12 and dot-lead couplings, one, two or three Fano peaks collapse forming bound states in the continuum (BIC). This partial (non-magnetic) swapping and the formation of BIC is found to result from an interplay of correlation effects and asymmetries in dot-lead couplings.