We report on the transport of mixed quantum degenerate gases of bosonic 87Rb and fermionic 40K in a harmonic potential provided by a modified QUIC trap. The samples are transported over a distance of 6 mm to the geometric center of the anti-Helmholtz coils of the QUIC trap. This transport mechanism was implemented by a small modification of the QUIC trap and is free of losses and heating. It allows all experiments using QUIC traps to use the highly homogeneous magnetic fields that can be created in the center of a QUIC trap and improves the optical access to the atoms, e.g., for experiments with optical lattices. This mechanism may be cascaded to cover even larger distances for applications with quantum degenerate samples.