Three-dimensional perfusion CMR requires acceleration methods to enable whole-heart coverage in short acquisition windows, which often rely on data correlation among adjacent time-frames. However, in free-breathing examinations, respiratory motion leads to inconsistencies in the shared data and compromises image quality. In this work, non-rigid organ motion is incorporated into a patch-based locally low-rank reconstruction algorithm as a transformation displacement field for each time frame. This motion-informed locally low-rank reconstruction, combined with Cartesian pseudo-spiral k-t undersampling, is proposed as a dual-sequence acquisition framework to enable quantitative free-breathing whole-heart perfusion CMR. Feasibility is demonstrated in simulations, and volunteers in rest and stress.