The extended molecular interstellar medium (ISM) is often witness to dynamically important events in the galaxy's evolutionary history such as outflows, inflows, tidal interactions, mergers, as well as dynamical structures affecting its current evolution such as large-scale bars and spiral arms. Studying the imprints of these processes in the diffuse, extended molecular gas is best achieved by a single dish telescope which can cover a large field of view with good sensitivity. In this work we present results from Atacama Pathfinder EXperiment (APEX) on-the-fly mode maps of two nearby galaxies: Circinus in the CO(3–2) line, and NGC 1097 in the CO(2–1) line, covering their full optical extents. We detect molecular gas at the largest extents seen for these galaxies yet, at upto 5' for Circinus, and 4'.5 for NGC 1097, and compute the total CO luminosities and corresponding molecular gas masses for both galaxies. We further analyze the large-scale gas kinematics through position-velocity diagrams and 3D tilted ring modelling using BBarolo. We detect notable features in both galaxies beyond their well-studied bright central regions: in Circinus we detect molecular gas embedded in a bar-like structure, and in NGC 1097, we observe tidal molecular gas structures likely involved in the interaction of NGC 1097 with the companion galaxy NGC 1097A. The presence of such previously unseen structures show promise for conducting future large-scale studies towards nearby galaxies with APEX.